The cheapest and best way is to softmod it... putting in a modchip is risky as you must solder points on the xbox board.
A softmod is totally reversible and you don't even have to open the xbox, (unless you want to add a larger HD, which is a whole other can of worms and unnecessary if you plan to just stream content from a PC etc.)
To softmod you just need a ORIGINAL copy of Mechassault game, (no platinum hits version), and a way to get a special savegame to a xbox memory card, (know someone with a modded xbox or a Action Replay?)
Modding an xbox to run Linux is legit, but the software used to encode programs like XBMC is owned by M$, making the software notlegit so I won't be able to help you there.
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