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If you want HD capture, I think the cheapest "good option" would be the AVERmedia capture card ($120 USD) but requires a desktop. I went with the Elgato Game Capture HD USB ($160) so that I could record to a laptop if needed.
There are cheaper non-HD options, but if you're serious about recording matches I'd strongly recommend the Game Capture.
If I remember you have to buy additional cords anyway.
The PS3 is encrypted HDMI
You need component cables to record no matter what.
I'd personally go with the Happauge. The older model is cheaper now if you can find it and since HDMI is encrypted it does exactly the same job.
Also may want to look into a video editing suite of some sort. There are some free ones out there that are just as good as the paid ones but require some learning.
I picked up a AVERmedia game capture HD for £60 with a 250GB hardrive. Best buy for a while. The only time you need your cpu is to transfer your files. Also Come with a remote . Not sure how much they retail at but its worth a look.