About 25, I'd say, to finish the game..
For plasma weapons per se, you need less than 10 (and these 10 is mostly the same guys as these 25 from above), but also tons and tons of other research, so it's almost irrelevant.
For decent armor... depending on your idea of decent armor. No armor in the game allows to take Heavy Plasma and Blaster Bombs with (even relative) impunity. One is coming close to it, but it's rather very hard to get and inflicts gruesome stat penalties.
As for the small fish... a lot of important techs can be gotten from like, 10, 20 or more sources, interrogations being part of these sources.