There is mo obvious correlation between no encounters and probability of success, but it looks like this is caused by better teams of adventurers taking on dungeons with more encounters on average.
 

There are no teams where more than 2 adventurers are of the same class. There is probably a reason for this.
Where there are duplicate types the dungeon is only beaten 55 percent of the time v 64 percent when there are no duplicates, so I will have 4 different types of adventurers in all my teams.
 

There is no obvious correlation between the rank of the highest adventurer and the probability of beating the dungeon. Suggests having a balanced team is more important than just maxing one out, unless there is specific evidence to the contrary.

Looking at the probability of defeating an encounter when a particular type of adventurer is missing suggests the following:
Goblins - teams do better than average when a Cleric, Fighter or particularly a Ranger is present
Goblin Chieftain - Teams with a fighter in them do much better than those without, Ranger is second best
Wolves - Are very easy to beat regardless of the team
Orcs - Fighters seem to be best followed by clerics
Orc Warlord - Teams with fighters do much better than ones without.
Orc Shaman - Again fighters are best, though mages and druids seem to be pretty close Skeletons - Easy to beat, though teams with clerics do a bit better than average
Zombies - Teams with clerics do best, though mages come close
Ghosts - Clerics  do best
Basilisk - Druids are best followed by fighters and clerics
Lich - Clerics are best followed by Mages 
Dragon - The toughest to beat. Fighters and Rangers seem best followed by mages and clerics
Boulder Trap - Fighters do best
Lever Puzzle Room - Easy though rangers seem do do slightly better than most
Riddle Door - Mages and Clerics do better than most, though again this is easy for all
Cursed Altar - CLerics do best
Snake Pit - Easy though Druids do slightly better than most
Poison Needle Trap - Rogues do best
 
Fighters appear to be the best all round adventurer, followed by clerics.
 
Looking at the probability of winning an encounter when particular levels of adventurers are present
suggests the following.
(1) When either a level 6 fighter, ranger or cleric is present an encounter against goblins is almost always
won. Rangers seem to be slightly better. 

(2) Where the highest rank of an adventurer is <= 2 the probability of defeating the dungeon is less than 50
percent. Between 3 and 7 it gradually increases from 61 percent to 68 percent, but there is a big jump to
87 when at least one level 8 adventurer is involved (Though there are only 30 cases of this).
 
 Temple of Lemarchland

There are 86 previous dungeons which had encounters which are a subset of those in the first dungeon. It looks very much like a junior dungeon. 4/8 teams which were all of rank 1 managed to beat it, which suggests spending relatively little on this.
 
 Infernal Den of Cheliax .

 The final encounter of every "Infernal Den" is either a Dragon or a Lich.
Every Den which has either wolves or Orcs encounters has a dragon at the end suggesting that we are
facing a dragon here. A high level figher looks like it is the best bet agasint dragons.
 
 
Goblin Warrens of Khaz-Gorond  

All dungeons with Goblin in the name have quite a few Goblin encounters, and most have a Goblin Chieftain. Poison Needle Traps, Snakepits and boulder traps are secondary threats.  Teams with at least 1 level 6 of several types look like they have nearly a 100 percent chance of winning against, lower level rangers seem like they are slightly better than other types. Fighters seem to be best against a Goblin Chief, though team with a
fighter with level > 3 seem to do worse than ones below it, though this is possibly a statistical artefact
as the numbers are relatively small.
 
I don't think I can confidentally identify a good choice based on my current understanding.. Peering through the fog my best current guess is:
 
Lost Temple of Lemarchland:
level 3 cleric
level 2 rogue
level 2 druid
level 2 mage
 
Infernal Den of Chelaix:
level 7 fighter
level 2 cleric 

level 2 druid
level 3 ranger

Goblin Warrens of Khaz-Gorond 
level 6 ranger
level 2 cleric
level 4 fighter
level 1 rogue

As abstractapplic notes, parties are less likely to fail on earlier encounters. I can think of multiple possible reasons:

1. resource depletion. Fights can deplete a resource (or possibly there could be multiple resources) and the party gives up when it runs out of the/a resource.
2. depth-dependent difficulty. Each fight is an independent binary check, but at a difficulty that depends on the depth of that fight.
3. debuffs. Each fight can apply a debuff that reduces success chance on later fights. Importantly different from 1 in what you can deduce from failure rate on a particular fight.
4. incomplete data. It's just too embarrassing to report to the guild that you turned back at the very beginning.

I'm proceeding assuming (1), but on a weak basis: it's the a priori most likely (imo), things don't immediately appear incompatible with this (without me having really checked), and the "Threat Level" stat seems most compatible with this. But I don't really know!

If resource depletion (at least, single-resource) is an accurate model, losses to an encounter type should be fairly informative about the difficulty of an encounter type and what is strong against it, with at least these caveats:

1. later encounters should falsely appear harder due to resources have been depleted
2. classes that are better at earlier encounters in the same sort of dungeon that the later encounter is in will falsely appear stronger in the later encounter due to having higher resources entering the later encounters

I am keeping these points in mind but have not really done anything to actually deal with them in the analysis.

I'm also assuming things like only the encounters in the dungeon matter and not the name, order of party members doesn't matter, etc.

edited to add: after posting this i did a brief check on the effect of levels and noticed two outliers where a high level party was defeated early:

Abandoned Dungeon of Azmar: Ranger 7 Druid 6 Fighter 6 Rogue 7 Snake Pit lich Lich (...etc, but defeated there)

Forgotten Temple of Stormwind: Ranger 4 Rogue 6 Fighter 5 Cleric 6 Basilisk Basilisk (...etc, but defeated there)

This makes me think a single-resource-depletion model is maybe less likely, and it might be a multiple-resource model (such that repeated encounters deplete the same resource), but I have no time to re-consider things.

• Goblins -> Boulder Trap -> Unknown x 8

Measure reports:

Encounters 3-9 are 2/3 Goblins and 1/3 Boulder Trap, and the final encounter is 3/4 Goblin Chieftain and 1/4 Goblins

I confirm, but go a bit further.  Dungeons with "Goblin" in the name all seem to have basically the same encounter generation, unless they have the "Night" prefix (in which case they can have Ghosts) or the "Mountain" prefix (in which case they can have Wolves). There are 118 Dungeons with "Goblin" in the name that have 9 or more encounters; all of these end with a Goblin Chieftain. Also, dungeons with "Goblin" in the name never have exactly 8 encounters, suggesting a discontinuity in the generation rules. Thus, the dungeon will end with a Goblin Chieftain (high confidence).

Threat Level: 3.95 (but beware potential bias regarding perceived difficulty of Goblins, reported by abstractapplic)

Goblins: Rangers are strongest.

Goblin Chieftain: Looks like a relatively hard encounter (but be aware of late dungeon bias).  Fighter is strongest.

Boulder Trap: looks like a relatively easy encounter. Fighter is strongest.

Ranger and Fighter are obvious choices. 

There are a decent number of very similar dungeons to this in the data. Restricting to dungeons with 7 or more total encounters including Goblins, Boulder Trap, Goblin Chieftain and no other encounters, there are 12 wins and 22 losses, maybe not enough to do accurate statistical analysis, but certainly enough for me to engage in my favourite pastime of overfitting to spurious  patterns.

Looking at these particular dungeons, Rangers look incredibly strong, Mages look very bad, and Clerics look uncharacteristically meh (they are usually quite good). Going by strongest-looking to weakest-looking and selecting the top four different types, it looks like Ranger, Fighter, Druid, Rogue would be the strongest party.

However, going further down the overfitting-to-spurious-patterns rabbit hole, Druids and Rogues together have a terrible record (1-9) on these dungeons. Note, Druids and Rogues don't seem to have particular antisynergy in general, so this is most likely completely spurious. However, double Ranger (2-1) looks better assuming the likely spurious patterns are real. Who to drop of Druid and Rogue?

Ranger+Rogue looks good, Fighter+Rogue not so much, Ranger+Druid and Fighter+Druid both OK, so Druid looks the safer choice. 

All of this, to be clear, is far too low N to be of any reliable use. But I'm doing it anyway because, whatever, maybe there's something there.

Another possibility would be Ranger+Fighter+ double Cleric, since both double Cleric parties won. But I'm sticking with double Ranger, Fighter, Druid. 

Levels: see below.

• Skeletons -> Poison Needle Trap -> Zombies -> Snake Pit -> Poison Needle Trap -> Skeletons -> Snake Pit -> Ghosts

Threat Level: 4

None of these look like particularly tough fights.

Skeletons, Zombies, : Cleric looks best, followed by mage.

Ghosts: Cleric still looks best, but mages look about comparable to fighters in distant second place.

Note: Ghosts commonly occur in both physical and undead-oriented dungeons, while Skeletons and Zombies are more restricted to undead-themed dungeons. So, potential for different biases to creep in from parties being weakened by other fights in different dungeon types.

Poison Needle Trap: Rogues do best, as reported by abstractapplic and yonge.

Snake Pit: Druids do best, as reported by abstractapplic and yonge. Possibly notable: Fighters don't look especially good here, despite Snake Pits commonly occuring in physical-oriented dungeons.

Obvious choice from just this info is Cleric+Mage+Rogue+Druid.

There isn't a big pool of dungeons with this exact encounter combo to look at for my overfitting. Although undead-themed dungeons with Skeletons, Zombies and Ghosts are common, and they often have Poison Needle Traps, they don't often have Snake Pits. In fact, dungeons with "Undead" in the name never have Snake Pits. However, Undead-themed dungeons without "Undead" in the name apparently have looser rules.

However, we can look at dungeons that have subsets of these encounters (with the understanding that the sample is low in Snake Pits).

Looking at this, Clerics, Mages and Rogues look good as expected, but next place is Fighter. Druids look quite bad.

If we look at synergies between these in this tiny data pool, all of Clerics, Mages and Rogues work well with each other, and while Druids still don't look as good as Fighters, they do OK when paired with these. So, I speculate that druids are only bad for missing something we needed more and we probably have what we need with this party, and that therefore taking Druid to deal with Snake Traps is probably worth missing out on whatever Fighter is bringing us on other fights.

So: Cleric+Mage+Rogue+Druid (same as abstractapplic and Yonge)

Level: see below

• Orcs -> Snake Pit -> Wolves -> Snake Pit -> Unknown

Measure reports:

The final encounter is a Dragon.

I confirm.

Threat Level: 4.5

Orcs: Fighters do best, then Clerics (as reported by Yonge).

Snake Pit: encounter is also in The Lost Temple of Lemarchand. Druids do best, as reported by abstractapplic and Yonge.

Wolves: Looks like an easy fight, but I expect this is largely because both Fighters and Druids do well against them, and since parties typically have 4 of the 6 classes the large majority of parties will have at least one Fighter or Druid. Fortunately, we are likely to want a Fighter for Orcs or a Druid for Snake Pits anyway.

Dragon: a very hard fight. No class looks to have a big advantage; Fighters, Rangers, Mages and Clerics all do comparably well/badly with Druids worse (by a bit) and Rogues worst.

There are few dungeons that are really close to this one, so only really looked at the individual fights.

If you look at parties with Fighters in them Rangers seem to  do better against Dragons than Mages, so I am thinking: Fighter+Ranger+Druid+Cleric.

I have not analyzed the effect of levels.  I will just slightly buff up the characters that seem the most important and on the dungeons I expect to be harder, and vice versa. I don't know the effect of giving different characters much different levels and will avoid that to avoid possible danger.

Solution (unless I change it later):

The Lost Temple of Lemarchand (9,000gp):

Cleric: 3

Mage: 2

Rogue: 2

Druid: 2

The Infernal Den of Cheliax (14,000gp):

Fighter: 4

Ranger: 4

Druid: 3

Cleric: 3

The Goblin Warrens of Khaz-Gorond (13,000gp):

Ranger: 3

Fighter: 4

Druid: 3

Ranger: 3