A good capture card is Dazzle DVC170.
I have one. and is in your price range.
Although with that quality of video it renders in MPEG format.
So youd have to buy an editing program such as sony vegas that is compatible with the file types.
Also if your in the UK youd have to edit the settings to NTSC because their is no PAL capture rate on the dazzle. NTSC and PAL are very close and you wont find a difference. Also, on the display when capturing the video, theres a 1 minute delay because of the amount of information being streamed through the USB. But that doesnt pose as a problem.
And depending on how your scarts hookup, you may have to buy extra AV cables or a scart splitter. Oh and also, your computer needs 2.0 USB which any normal computer should have, and youd need a nice bit of RAM to run it, just make sure you check it on the system requirements on the box.
Aslong as the capture card is connect to the PC and the xbox and the television, itll work.
One last thing, you cant film in HD with that capture card, so one downside is that you cant play in HD when your filming.
I think i covered everything.
Happy gaming :]