If you mine with a pool, your actual internet activity will be fairly small. I just took a look at my network statistics and BFGMiner used 9MBytes down and 11 MBytes up over the previous 24-hour period.
The Bitcoin-Qt application on the other hand maxes out my upload bandwidth since I always seem to get 2-3 peers who want to download the entire 12 GB blockchain from me. Other than that, the main Bitcoin-Qt network usage occurs when you are receiving or relaying the latest block (blocks are typically 100-400 KBytes).
Since you have limited internet bandwidth, your best bet would be to run a lightweight client such as Electrum or Multibit. If you are mining in a pool, you don't need a local Bitcoin-Qt.
Will you be solo mining or joining a pool? – Nate Eldredge – 2013-11-27T00:48:11.923
If you make enough from mining you might still make a profit and be able to pay for the extra charges :p – Broseph – 2013-11-27T01:39:04.937