I have batched a couple hundred videos from wmv to flash using the encoder that comes with Flash 8, and it worked perfectly. I recommended going into settings, Show Advanced Settings, and lowering the audio quality down to save a bit on bandwidth, and to tweak the video quality to your liking.
And as mentioned by Konda, this is a good flash player to use, and it has the option to play at full screen.
http://www.jeroenwijering.com/?item=Flash_Video_Player
Make sure your server can handle the number of simultaneous streams you expect to have. Flash can put a performance hit on your server. I don't recommend trying to run many streams on a shared hosting plan. You'll spike the server real quick and create problems with your site loading.