Minimal Internet usage on an Android phone
Depends entirely on how many contacts you have, how often they change, how often you set it to sync, etc.  Paying for data as you go is generally a bad idea with an Android phone, they use a lot.

You should be able to shut off 3G though (probably dependent on the phone) and just use WiFi.  Although, it might be more difficult to prevent it from using 2G data.  Some phones let you use WiFi while the phone is in Airplane mode, which would shut off both 3G and 2G.  Android has the ability to store WiFi credentials and connect automatically.