I was looking for a faithful experience, but wanted to take advantage of mods to improve the experience.

I read there are just bug fix mods, visual upgrade mods, and some that do both, like the GMDX. Is the latter worth it? Or should I try the mod that is available in the gog download page?

What do you recommend?

Go with this. The final version just came out a couple weeks ago.

http://gmdxmod.com/

Yes, go with GMDX first. It fixes many bugs and vastly improves the gameplay and controls, the gunplay is now miles better than in the original, stealth and AI behaviour are also much improved. The mod stays quite close to the core experience.

Revision is also very good, but it makes substantial changes to the levels, so I'd leave that for a second playthrough. The gunplay in Revision is not as good, visuals are slightly better than GMDX though.