Once you've eliminated the unsuitable, do -not- pick the "best". You're probably pretty good at identifying what won't work, but you're probably pretty terrible at identifying what will.
I didn't quite understand this, could you please elaborate?
Your ability to judge both yourself, and another person, and how your personalities will interact, is limited. It's sufficient to identify people with whom you absolutely will not get along, with reasonable accuracy; this is low-hanging fruit. So let's say you've eliminated 95% of the candidate pool by this point.
The remaining 5%? You're now considering a pool of candidate partners who you can't immediately eliminate (assuming you have more than one person remaining, after all probably-unsuitable people are eliminated). At this point your list of candi...
Speaking from personal experience, finding the right relationship can be HARD. I recently came across a rational take on finding relationship partners, much of which really resonated with my experiences:
http://waitbutwhy.com/2014/02/pick-life-partner.html
http://waitbutwhy.com/2014/02/pick-life-partner-part-2.html
(I'm still working my way through the Sequences, and lw has more than eight thousand articles with "relationship" in them. I'm not promising the linked articles include unique information)