So Far every game of the regular season that I've seen has been broadcast in full HD. Beautiful picture on my monitor. As for the streaming bandwidth question, I'm not sure. But, using my system as an example, I Use a wireless connection from a cheap $50 linksys router connected to a 9 yr old cable modem with standard cable internet service from cablevision (my local provider) and have no problems with the streaming. The only time I've noticed a tiny bit of lag in the video is when I have the mlbtv video up at the same time as 2 yahoo stattrackers and my windows media center TV on (to watch the local blackout games), and thats solely on account of the memory on my comp being maxed out (5 yr old comp with only 2 GB of memory), not on the connection. I highly reccommend it.
PS... If you get it, make sure you definitely get the premium service, otherwise you wont receive full HD streaming, and you wont be able to watch multiple games at once, or use the Picture in Picture. Definitely worth the extra couple bucks.