I'm not very familiar with the wmv rendering options within Vegas, prefering to use the Microsoft engine instead; however, you can choose to encode an avi file into wmv with the adjustment of a number of parameters. One, for example, is the window size. You can pick a little postage-stamp size, a medium size (such as 240x320), or large.

Then you can also adjust the bitrate. If you've chosen the tiny window, then perhaps 40Kb/sec (dialup) would be an adequate bitrate to make the video look good. Such a bitrate with a medium-sized window would produce pretty horrible video, with lots of blocky artifacts.

When I was encoding to wmv, I would use 240x320x30fps and I found a VBR of about 200 or 250Kb/sec delivered reasonably good-looking video. I don't use wmv any more, since I've concluded that Flash8 is much more browser-friendly. But in Flash, I need to bump that bitrate up a little in order to match the wmv quality. I think the Flash8 videos on the choir website that I maintain run at about 300Kb/sec.

The bitrate you choose, of course, depends on the size of the pipe your viewers will be using to get the data. Somebody on dialup will be very unhappy with my 300Kb/sec video, since his player will run for a few frames, then freeze for 10 seconds, then run for a few frames more. But most of the people around here have broadband of at least 256K.

EDIT:
I may have missed your basic question. When someone's browser clicks to your web page and there is a video player embedded on it, then depending on how you've set up the player on the web page the player will either just sit there and wait for you to hit the play button, or it will immediately begin asking for video data from the web server. I set up my embedded Flash players to just sit there, so that the rest of the web page loads quickly. When the user clicks the play arrow, the browser begins requesting video from the server, and the server delivers that data as fast as it and the pipe in-between will allow. On my Flash8 player that I use, you can see at the bottom of the player a black line superimposed on a grey line; the grey line shows how much of the whole video file has downloaded to your PC, and the black line shows the current play position. You can see it here.