One crucial recommendation is to shave upwards from the bottom of your neck to the top. This takes a lot of getting used to and really gave me the willies at first, but it works much better and you miss a lot less hair.

Really? I have the exact opposite experience. I find that going against the grain, especially on the neck, gives me nicks and rashes.

After having experimented a lot, what works for me is wetshaving using any ol' shaving cream, multi-blade razor, going with the grain.

Since facial hair grows in different directions this means you have to pay attention to it. Briefly, I shave top-down on the face and away from the chin on the neck.

For a very smooth shave, I sometimes do it with the grain, a second time against the grain and a third time with it. I read somewhere that the third time is important to avoid ingrown hair and rashes and in my case it works, but YMMV.