hey,
i'm doing just that. i was kind of in your situation a couple years ago. after finishing 2 years of college i had no idea what i wanted to do. i decided to try to get into the Air Force Academy, but once i got in i decided to do AFROTC instead (my parents promptly had a simultaneous heat attack
). So, I've been involved with AFROTC for the past two years and will be an officer in december.
your questions seem to be more of a general variety, i'll try to give ya my .02 on what i can... please feel free to post questions or pm me if there is more i can help you with.
don't think of yourself as a leader? well, i would say that would be the biggest reason i can see from your post not to join. even if you don't think of yourself as a leader, everybody else sure friggin will... you'll have to perform accordingly. there are a lot of benefits in being an officer (more responsibility/respect, decent pay etc.) but the expectations from your airmen and peers will be high. once you join the AF in any capacity, get ready to be constantly challenged and evaluated on everything you do.
AFROTC has mostly been a good experience. I've spent two years at my local detachment. Our program requires 2 early morning PT sessions a week plus a 3-hour credit class and a "Leadership Laboratory" (where all the cadets gather for a corps-wide exercise). in the summer you'll have to attend a 4 week field training unit. it's kind of like a prospective officer's "basic training" only with a leadership twist. you won't be there merely to survive, but also to be evaluated on your leadership and stress enduring qualities. it isn't that hard, but it weeds out the undesirabels to a certain extent.
your other option would be Officer Candidate School after college. it's a 3-4 month long intense course that is basically AFROTC all squished together.
as a math major you'll have some leverage, but don't assume you can just walk-in and join. for officers, there is a vetting process. joining the officer corps in the AF is a competitive enterprise. there are limited slots and far more people who apply than get accepted. our force-shaping goes on, so the demand varies from year to year according to the "needs of the Air Force" (something you'll hear often.)
hopefully this will help ya out a bit. please post on this thread again if i can help ya out more. i think i would've valued an opinion other than a recruiting officer's when i joined. good luck to ya.