Sorry I missed your question. To be honest, the Wii controller can sense the speed of the movement, but most reviewers have already stated that in all of the games so far, you can just as easily pull off the moves with very slight flicks of the wrist as you can swinging a long looping stroke. That leaves it up to you as to how involved in the game you get as far as the motion of the controller goes. Now that doesn't mean that later on developers can't program in more sensitivity into the Wii remote and sensor bar, but for now, there's no set way to swing the Wiimote.
I played some Wii Sports Tennis, and it made the same movements whether I swung the Wiimote in long strokes like I would a real tennis racket or just flicked it very slightly with my wrist. The Wii sensor bar does react to the 3-D space between it and the Wii Remote so it's definitely possible to MAKE players have to use accurate strokes and movements of the Remote, but so far, doesn't look like any games are making serious use of it yet. Maybe in time.
As for the other question, you just need a broadband connection. A computer is not necessary. You will need the LAN adapter if you plan to plug a cable into the Wii, as the Wii only has built-in Wireless, which would mean you'd need a wireless router of some type in order to use it.