It depends on what you want to caulk, but I'll give you a run down:
Your major options are silicone, siliconized (acrylic) latex, and (acrylic) latex. There are other options that are elastomeric for flexibility and speciality like for flame resistance.
Silicone is difficult to work with, but stays put for a long time (usually very long warranty). Another advantage is that it comes in colors. Clear, black, silver, gray, white, even greens, reds, browns, and oranges. Silicone's other advantages are that it's paintable and fairly flexible so it resists cracking.
Latex is easy to use and clean up. This is its main advantage. It comes in limited colors (usually clear, white, bisque, almond, biscuit, etc.). Latex is not paintable. It'll do for indoor projects and is pretty inexpensive.
Siliconized latex is generally what you'll find if you just pick up a tube of caulk. This is, in theory, the best of both worlds. It's easier to use than silicone and although it comes in limited colors, it is most often paintable. It typically doesn't crack either, like its silicone-only cousin.
That said, my personal recommendation for general use is siliconized latex caulk. Specifically, DAP brand ALEX Plus (that's A-acrylic and LEX-latex) is fairly inexpensive ($1.50-2.50 per standard tube) and will do just about anything. Indoor/outdoor, paintable, easy to work with. And I believe the warranty on the ALEX Plus is 50 years.
The only other thing I would recommend is that if you're going to use it around a tub or sink, that you get one with an antimicrobial additive (Mircoban, EcoGuard, etc.). You can usually pick these up for $4-5 a tube, but it greatly inhibits the growth of fungus (molds and mildew).
If you want adhesive, keep in mind that while caulks tend to have adhesive properties, you can buy a general construction (or specialized) adhesive like a Locktite Powergrab, a PL 200 (or other varities: 300, 400, etc.), or of course Liquid Nailz.