The full Opera browser is currently free. Wii is a WiFi system, it doesn't come with any Network Cable ports. It has USB ports that you can probably get a LAN adapter for if you need it, but otherwise if you have wireless access already you can set it up for that. The speed is ok I guess, I haven't really noticed any sufficient load times. (The DS Opera browser, however, is slow as hell.)

Another thing about the online is WiiConnect24. You can put your Wii in sleep mode, and people can send you messages and stuff while it's in that state and connected to the 'net. When you receive a message, the Disc slot pulses in this sexy blue light. It's pretty cool. Nintendo also sends you messages, like informing you of new channels available to download or new firmware updates.