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
I will probably start with Nicehash to get my feet wet then move to mining solo
For Nicehash you will probably need more than 10kb/ps and a requirement from the official Nicehash page says that you need a stable internet connection. Based on my personal experience a minimum of 4Mbit/Sec is the ideal speed if you want to also browse the net or use internet for other things while Nicehash does its own thing.