Where my rig will be placed there is no internet. I have an AT&T USB modem that is getting around 6MB down and 3MB upload speeds. Will this be sufficient?
Depends if you're going to mine in a pool, or solo.
I've seen people saying that 10kb/ps is enough for pool mining, since you only need to send the work in and out?
This answer might be a bit more indepth. See
https://bitcoin.stackexchange.com/questions/360/what-are-the-bandwidth-requirements-of-a-mining-rig