The 3 different grips you mentioned will all work both your back and your biceps, but to different degrees and in different areas. Pullups with a shoulder width or slightly wider grip will target your lats and, to a lesser degree your middle and upper back and biceps. A neutral grip or a chinup style grip with palms facing you, will still work your lats, but will shift the stress more towards your middle back and your biceps.
A lot of people will alternate grips between workouts to get the best of both worlds. If you're just starting out and aren't proficient at pullups yet I suggest sticking with a pullup grip until you can crank out a few good ones, and then start switching grips. This doesn't mean you can't throw in a few neutral grip pullups or chins in your workout, just concentrate on the regular pullups for starters.
Some pullup tips in addition to the ones posted by Kevin on this site and by others in the forum:
- instead of imagining a pulling motion, try and imagine pushing down with your elbows. This will help you to engage your lats to raise your body instead of just your arms
- if you're a heavier guy (or even if you're not for that matter) keep your movement controlled and don't let yourself drop fast to a dead hang at the end. The negative motion will help train your grip, help train your back, and save your elbows and shoulders some pain. And by controlled I don't mean very slow. Keep things moving at a smooth quick pace.
A final thought: I'd stay away from really wide grip pullups since it can aggravate your shoulders and the shorter range of motion won't do you any favours.