Xbmc is built with the (leaked) microsoft SDK which is not licensed to homebrew people. There is a fully homebrew SDK available but it is not quite as nice (it works but the MS one is arguably better) and by the time it got good enough for people to use the SDK MS made was used almost exclusively for all homebrew, each of which would require a fairly significant rewrite.
Still
There are many ways to install xbmc and you have two options as to how it works:
XBMC as a dashboard (i.e. it boots to xbmc)
XBMC as an app (i.e. you run it like you run an emulator, app or game).
Personally I like xbmc (I use the 360 lookalike skin mainly) as a dashboard.
The easiest way I find is to use AID (autoinstaller deluxe) to install it (the most recent AID has a really nice version though) and then use the upgrade script with a network connection.
Look around the xbox and you will probably see a .xbe file or two. One of these is the dashboard and will need to be replaced, there are a couple of ways this could go down though so I suggest you read
http://xbmc.org/wiki/?title=As_a_Dashboard
Upgrading can be done by script or by FTP/some other transfer method.
The advantage of FTP is you can drop skins if you want the space.
As for discs vs drive (I assume network is out of the question) there is a bit of a debate.
Drive: you can dial up a series, show, film, album..... whenever you like (hence the get a remote part) and aside from the electricity (and if you count it wear on hardware) it is free,
Disc: assuming you have a good drive (some of the earlier xboxes are not so good
http://www.xbreporter.com/xboxdvddrivecomparison.php ). You burn discs though which have the advantage of being able to be used by near enough everyone (who can not play a bog standard avi these days).
Personally I strike a line between HDD (I tend to take my xbox with me when I go places), discs (I like a lot of shows but only watch them once every couple of years), my USB stick (it is only a gig but for hot off the press stuff it is great) and network (nice but I can not always use it).
Games (as in official). Sometimes they are quite big (later games went well over 7 gigs although rips exist).
Trainers are easier to apply as are hacks, courtesy of the xbox not being very big in Japan you are probably not waiting on too many exclusives to be translated.