01-28-2007, 12:30 PM
I'm afraid I can only help with some of this, since I don't watch ANY sort of TV from my computer.
First of all, the Airport Extreme is simply Apple's brand for a WiFi capable router. The Airport Extreme supports 802.11, 802.11g and the new draft (not yet fully certified industry wide) 802.11n. The "draft n" version is important because it allows transmission of up to 100 Mbps over the air, the same speed as many of today's wired routers. The fact that it is not certified industry wide is of no consequence if you buy "draft n" routers and "draft n" capable computer from the same vendor, in this case Apple.
802.11g, with its top speed of 54 Mbps, was said to be just BARELY able to handle streamed TV adequately. 802.11n is said to do a very nice job of it. That is why Apple released both Airport Extreme and Apple TV together. You need both for a good experience.
The Apple TV is clearly aimed at streaming TV, but will do audio media as well. According to Apple's web page on its connectivity:
it is capabile of HDTV up to 1080i - note the "i", not the most demanding form of 1080, which is 1080p.
Again according to this website, it will only stream stuff from iTunes, but remember, iTunes is really just a media management program. This doesn't imply that it will only play stuff you bought from the iTunes online store. It will definitely play MPEG4's ripped from DVDs for example. I have done that myself.
Re the mini, it is a full fledged Mac, as I am sure you are aware. So it is a free standing computer, rather like a PC, needing only your keyboard, mouse and monitor to work. It is the low end of the Mac line, featuring slower processors and shared memory graphics. It makes a great general purpose Mac, but don't plan on using it for really demanding stuff.
I'm afraid I can't help much further - I am not aware of ways to directly connect your Mac to your TV via firewire or other techniques. This doesn't mean that you can't do it, just that I am not aware of it.