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 to cut off your 3G altogether. Take a look at: How can I prevent my phone from using any kind of internet?How can I prevent my phone 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.
