Main problem. Upstream bandwidth. 2Mbit is about enough for standard xvid in terms of download rate although high action will mess things up, 5Mbit is what I consider a bare minimum and 10 is OK. Getting this from a US ISP is practically unheard of for a home user (business types pay through the nose for such options).
You have two options though and they mirror standard home networking/video distribution. There you have the option to essentially make a file server and the option to make a transcoding setup and stream via a given protocol (discussed below).
You say TV which complicates things a bit, most TV capture cards are tied into odd software and trying to get them to work properly takes some effort or using an app like mythtv. A note, old style analogue TV (which I understand is ending shortly if it has not already) needs to be encoded while digital* is broadcast in MPEG2 format usually (varies a bit depending on where you are).
Also streaming them live can be a bit of a problem so I suggest you plump for an option that causes a few seconds of lag compared to the live stream (if you are willing to suffer 15/16 minutes delay at the start you can probably kill the adverts too) and encoding that in a better format. A channel/time selector is not hard to wire up to it if you get that far (digital TV broadcasts many channels in one stream).
*it gets far more complex if you tie drm into it and bypassing such things is another topic entirely.
File sharing:
I do not suggest running an FTP site or similar but virtual private networking should do the trick (your internet connection essentially allows people to join your network as if they were in the same place as you).
VPN. Something like hamachi (normally used for games) may work but it will be tricky if it does not so I would suggest a full fledged vpn first.
Actual streaming. You can do this directly off your machine or you can use it in conjuction with the methods above.
There are a few methods to do this although the main ones are
flash: seen in youtube and similar sites the world over. Quality is barely passable in my opinion.
windows media: used in higher quality situations although you are usually restricted to MS software (codec level, you can use stuff like VLC still to watch).
quicktime: goes from flash level to windows media. Mirrors the likes of windows media when it comes to playing it.
real: I do not rate the quality as highly as the others but it is probably better than flash. Software is real player (generally given as the ultimate example of bloatware) or hope real player alternative works.
Those are the big 4 but you also have the likes of divx as seen at the now defunct Stage6:
http://labs.divx.com/Webplayer
As it stands only divx have shown what can really be done quality wise (bitrates between a decent youtube video and an xvid one are not that far apart), everything else is a de facto standard of sorts that people are reluctant to move from and suffer the consequences of. It is also a matter of the contained used: AVI files have an index at the end of the file (why trying to play an incomplete file has issues although very functional workarounds exist) while any self respecting streaming format will play as it comes down.
As an aside you could theoretically rebroadcast the transport stream from your digital TV although all but university connections will have difficultly pulling that off in real time, transcoding to a lower quality (and size) is an option but not one I would consider in light of the alternatives.
Next option is a delay using standard files and chopping up the encode with an automatic playlist of sorts: you encode 15 minutes as one file and while watching that the next 15 is encoding and so on and so on.
Over to you, if you want specifics we need more info.
JM 
