Soft rubbing probably won't hurt it. Pressing it too hard, though, can burn out pixels. If you've done this, you'll notice little dots of black (pixels that aren't lighting up) fairly soon.
Check
this information on LCD screen protectors. When they get dirty, just pull them off and put another on.
If you don't decide to do that, it's best to use a
wipe specifically designed to clean LCD screens. They have a solvent (if that's the right term for what it technically is) so you don't have to push as hard to clean smudges and grime, and it's known to be safe (Windex, for example, is not safe).
