I have a limited amount of data included in my internet plan. If I exceed that limit I get charged extra. So, before signing up for Bitcoin, I'd like to know whether Bitcoin mining causes a lot of internet traffic. Does it involve a lot of downloading and uploading throughout the day?
If you use a light wallet like Electrum, definitely not. But even if you run a full node, it is unlikely. You could also use a web-based wallet like blockchain.info which would mean that nothing at all is running on your local computer and you can access it from anywhere.
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.