I have wired my entire house for component video + stereo audio using copper core (solid copper, not copper clad steel) belden RG59 coaxial cable. To run component video, you will need 5 cables end to end. I run my own bare cables then terminate with RCA connectors (then to wall plates) then build flexible patch cords for the actual hookup.
The "cheapest" way to do this (and still get very good results) is to buy pre-made coaxial cables (like for hooking up your cable box) of the correct length (you can get 50' + at places like Home depot or radioshack) and use F-> RCA adapters on them. This will give you great results and not cost a ton of money.
If you want to go a bit more custom and possibly (but not guaranteed) better quality, the buy a spool of RG59/RG6 that has a solid copper core. The rest of the specs are not as important, as long as your runs are less than 100' or so. Once you get to longer runs, you need to be more critical of cable specifications, but for shorter runs it's a non-issue. Then buy some RCA connectors (designed for that cable) of either the crimp variety of the compression type. DO NOT under any circumstances use the twist-on type. They are total crap. You will need to purchase or borrow the proper tooling to strip the cable and attach the connector, so there is a cost overhead here. If you are going to be building a lot of cables, then this is a good way to go, but otherwise, I'd go with the pre-made coax cables and adapters.
If you're going HDMI/DVI etc, then that's a different story....