The most critical parts when recapping

They are all important in terms of sound quality. However, and this is a big however, in practice you will find a lot of them very hard bordering on impossible to replace. That is because the really good caps are always really big. They simply will not fit where the old cheap small ones did. Also the cost gets out of sight really fast if you do that. So in practice you replace the "big" caps, basically the power supply caps, and however many others you can afford and fit in there.

The biggest bang for the buck however is diodes. Here you can run into a similar problem but not as bad as caps, but if your replacement diodes have heat sinks they may need to be modified to fit. Its all worth it however as faster/better diodes remove a huge amount of grain and glare, with pristine high end extension, and a deeper more expansive sound stage. Diodes in my tube amp were my first mod and I was staggered.

The difficulty with diodes is that like caps they all sound a little different. But unlike caps which everyone knows affect the sound for some reason hardly anyone gets that about diodes. Michael Spallone definitely is not one. He mods Synergistic MPCs for guys like me with Active Shielding and after trying a few diodes found ones that are pretty amazing. Unfortunately he's guarding his secret sauce! Since I know the value of this I found it worth paying him to do the mod. (A very simple mod, but I don't want to do it 5 times trying different diodes, so had him do it.) In your case I would just look around and find the fastest smoothest ones and call it good. They are cheap and will almost certainly be a lot better than whatever's in there now.

Resistors, don't bother. Its not that they don't matter. Its that they don't matter as much, and in some locations not at all, and its hard to know the difference, so not worth the bother. Now someone will come along and say different. If they can tell you what and where, go for it. Every little bit helps.

Thank you both for great input! This really cleared it up for me. 
About diodes:
Do you also here look for the same "values"? Or are there aspects to them that you can change?

Luckily, in my project now, I actually have replaced the large power caps, and a set of four around them. There are a bunch of tiny caps, like 10uf 50v. Worth swapping out?

As far as I can tell everything everywhere makes a difference. When you ask about is it worth it though, hard to say. Mostly because with caps there seems to be no upper ceiling on cost. Plus there's little tricks like using better large value power supply caps and then adding one really crazy good one of smaller value on as a filter cap that doesn't really affect the power supply except to greatly smooth the last tiny remaining vestiges of ripple. 
 
With diodes I would stick with whatever's in there. With diodes, if I got it right, its all about volts and watts. Watts being the heat dissipation part. What you're really doing with both caps and diodes is finding faster ones. With caps they don't really have a way of measuring but with diodes since they cut on and off they can measure switching speed and graph it and so you're looking for the one with the steepest fastest response and also the smoothest noise-free response. Because switches, which is what diodes are, tend to spike. You want fast but no spike.

You find a really fast smooth diode, that's your huckleberry.

There are a bunch of tiny caps, like 10uf 50v. Worth swapping out?

Yes, any electrolytic on the power supply rails is worth swapping out to prevent them from shorting down the road.  I used to use Panasonic FM for these, since they were reasonably affordable and had low inductance, and therefore high noise blocking.

There are a bunch of tiny caps, like 10uf 50v. Worth swapping out?

If you have the time and skill, replace all Electrolytic Capacitors, they 'age'!
Relays on amplifier protection circuits also caused problems went they get old.