Hey Matt,
Like ChrisH, I'm a cross utilized agent. I basically do everything from working the ticket counter, ramp, cargo, baggage service, etc.
Most airlines have both part time and full time positions available. The best place to start looking for these positions is by going to the website of the airline you are interested in and look for the careers page.
Regarding flight benefits, again, most airlines offer them to both part time and full time employees. The benefits range from free travel to ID or industry discounts on other airlines worldwide. For example, in December of last year I traveled to Sydney, Australia. I was able to travel in business class round trip for a grand total of.........$300!
Just for fun I priced what a RT business class ticket would be for the same dates I left and came up with $10,000. It's amazing when you look at it that way!
As for baggage handling, I would assume at a major airport that would be your only task. Your duties may include running bags from airplane to airplane, sorting, or loading them on the aircraft. Again this all depends on the airline and airport you are working for.
Overall, I love my job. I've been doing it for about 3 years. I'm a full time student at the University of California Santa Barbara and have been able to work my schedule in conjunction with my school schedule. Some days are really fun and others are down right bad. I've figured out that if you do work for an airline, USE YOUR TRAVEL BENEFITS! You must be able to step away from the industry every now and then, you sanity depends on it! LOL
Hope this helps...any other questions let me know!