1) Any ohm range that would be applicable to the resistance you are measuring. You can't hurt anything by going over or under - if you go under it will just show 1. (meaning that the resistance is over what can currently be measured), if you go over you'll just lose precision and can step down the range to the correct one. Headphones are generally 32-600 ohms (some are more, a few may be less).
2) The easiest way to determine ground would be to place one probe on the ground of the jack (the "sleeve" portion of the jack, farthest from the tip), and then probe the other wires for continuity (your meter should have a continuity setting where it buzzes - if not, just set to the lowest resistance range and look for near-0 resistance). A multimeter should not damage headphone drivers AFAIK.
Most headphones have only a single ground channel (shared between left and right), unless they are high-end "balanced" headphones. What pair do you have?
Nice to see someone else from UCLA on the board!
Edited by Juaquin - 6/6/10 at 6:30pm