You have a few choices for getting YPbPr component out of the Xbox. I think the top recommendation right now is the XOSVP (Xbox Open-Source Video Project), which is an open-source alternative for the official HD AV Pack breakout box. They come in either preassembled or in kit form, though, unfortunately, they both appear to be sold out. A potential downside is that this kit only offers S/PDIF audio via TOSLINK; so, if you can’t accommodate that and need analogue stereo audio, you’ll need to either add a TOSLINK to RCA converter to your budget or pick a different solution.
The next-best option, I think, is the official HD AV Pack. These mainly came in the form of a breakout box with separate RCA-to-RCA component cables, and offered YPbPr component output, as well as TOSLINK for digital audio and stereo RCA for analogue audio; but there also was, at one point, a version of the HD AV Pack that was an all-in-one cable that had a TOSLINK output molded into the AV connector. I think some people found these breakout boxes to be prone to visual noise, and the cables were not of good quality; but I have one, with the original cables, and, if those claims are true, the issues are not pronounced enough for me to notice. I don’t expect the latter, all-in-one-cable version to suffer from those issues. These solutions are growing in rarity, so expect to pay at least $65 for one in good condition.
Finally, the budget option would be to pick up a cheap, third-party component cable. I had successfully used one for years without issue, before moving to an HD AV Pack because I wanted digital audio. I might have just stumbled upon a decent cable (bought from a used-game store years ago). If you go this route, stay away from anything Tomee-branded; they’re known for making thin, noisy cables.
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