I connect to internet on my E51 using one of these methods:
1. Wifi - this mobile has one hell of a signal strength, especially if you disable the power saving setting in the Access Point of your wifi profile (settings->connection->access points->your wifi profile->advanced settings). To save some battery, once i connect to the wifi, I switch off the scanning from the front screen.
2. UMTS/3G/HSDPA - this is also known as packet data and which costs you money per MB downloaded/uploaded. I normally disable this when I am connected to wifi (just in case!) by going on settings->connection->packet data->high speed packet access->Disabled.