Wirelessly posted (Tmo's cheapest BB customer)
I also have a 8320 and didn't have a data plan during the first year when I had the device. Unless there's some new rule in place at Tmobile, you should be able to browse over wifi without having to get a data plan.
Check your service books to make sure you have the 2 for wifi. Also check your browser under Options>Advanced>Browser to make sure you have selected the correct one.