How do I actually get this mods to work?
Where do I activate and use them?
I've read about mutators and things in other places. Do I need that?
At first (if you didn't do so already) install the official 1.1 Patch and then the actual mods.
Some mods (like KM/ BCSupermod and i think DS9FX) include already things like Foundation
which you should DL(newest version is included in BCUT 1.2) if you don't use the above mentioned. If you use the above ones, only use one per install as they are incompatible (aside KM 1.0 includes DS9FX).
Second (and third as they are the same): Yes you need Mutators. those "activate" most mods after the installation. I think there is a stickys thread somewhere here about those.
Recommendet Mods, hmm. I personally use KM as Backbone of my install, as the included mods are altered for max Compatibility (spelling??)
If you want to Play the Singleplayer Campaing I would suggest to use BCSupermod as it was intended for this.