ok, well to answer your first question, I believe that a display needs to be able to output at least 720p to be considered HD, 480i is Standard Definition, and 480p/ 720i is Enhanced Definition.
Right out of the box the wii console only comes with standard a/v cables. If you've got a high end tv and want the best picture out of it, then you'll want to buy a set of component video a/v cables. These are readily available at most retailers, and will run you anywhere from $29.99 to $59.99 depending on the brand you choose.
Now, about internet capability and online play:
You need to have Cable or DSL high speed internet service.
The wii is wifi enabled, and is relatively simple to connect to any existing wireless home network. If you don't have one, a good wireless router can be had nowadays for as low as $30.00 Your other options are 1. If your wii will be set up relatively close to a computer that is running windows xp sp2
you can buy nintendo's wifi usb adapter which connects to any available usb port on your computer, and is very easy to set-up, and 2. if you've got an open port on any network hub or switch, you can buy a LAN adapter, which will give you a wired connection, and the fastest data transfer, both the wifi usb adapter and the wii LAN adapter cost $29.99
Use of any and all online services on the wii are free(but you are already paying for internet service, so it's not really free)
Right now, and until sometime next year, you will not see any online multiplayer games for the wii. So right now, you cannot play online.
There is still plenty to do with the wii- you can use the wii shop channel to download the internet channel, the forecast channel, and the news channel which let you browse the internet, get live weather updates and news updates. and of course, you can download some great classic games for the wii's virtual console.