You can definitely connect to WPA protected wireless and your phone will connect automatically when you're within range of a known wireless network. 

You can use [APNdroid][1] to cut off your 3G altogether. Take a look at:
https://android.stackexchange.com/questions/5273/how-can-i-prevent-my-google-g-1-from-using-any-kind-of-internet

If you've got wireless at home and you're there every night, your phone will be able to sync your contacts, etc. over night. 


  [1]: https://code.google.com/p/apndroid/