I'm currently running my PS3 via Component Video and it's fantastic; I started a thread about having trouble with HDMI (though that's irrelevant for you). Anyway, PS3 is definitely good to go with green-blue-red.
Be aware that, for both PS3 and Xbox, some games run at 1080i (for PS3 even 1080p), and some run at 720p. I would set the PS3 Display Settings so that 480p, 720p, and 1080i are checked. The PS3 will acknowledge this as "a maximum resolution of 1080i". The main PS3 menu thing will run at 1080i, and it will run games (if the game does not override the Display Settings) at this setting, such as Gran Turismo HD (which allows you to specify 720p, 1080i, 1080p, or the PS3 settings). If that works, which it should, uncheck 1080i so that 720p is the max res. This will be interesting, as this ought to test the tv's ability to accept a 720p signal, which the tv should in turn convert to 1080i (or 960i) using its own video processor. I can't predict whether this will work, particularly because my 2002 tv said 1080i/720p/480p on the back.... However, it's worth trying because I've noticed that with the game Call of Duty 3, despite it clearly saying on the box: "Supported HD video output: 480p, 720p, 1080i", if 720p is not checked in the Display Settings, the game reverts to 480p. I consider myself fairly knowledgeable in this area and I cannot force the game to run at 1080i (much to my dismay, cuz it's a gorgeous game, esp. level 10). I don't know whether this is a problem with the game or the PS3 itself, but after shelling out $50 for it, I would have been pissed to find it not running in HD. If you don't have Call of Duty, you can download the Motor Storm demo for free from the Playstation store, which is also where you'll find the Gran Turismo HD demo. Motor Storm also prefers to run in 720p, and thus if 720p is not checked in the Display Settings, it will default to 480p.
I'm rambling here, sorry. Basically, in the Display Settings, see what you can get away with. On the screen where you check off the different resolutions, you can push SQUARE while highlighting a certain resolution, and it will test that resolution for you; you'll know if it doesn't work and just press CIRCLE and it'll go back to whatever resolution it was using before. See if 720p works despite it not being listed on the back of the tv. And this will save you the time of downloading stuff, too.
I know all these numbers and letters are confusing. The number simply refers to the number of vertical lines in the signal. Higher is better, as a general rule, though this is the topic of much discussion, as the letter paired with the number is not insignificant. However, for you personally, considering your sources and your "necessity" for HD, I feel comfortable saying that 1080i will server you just fine. If you want to test 1080i using an actual game (not just the PS3 main menu), download Gran Turismo HD. If 1080i is selected in the Display Settings, it WILL run in 1080i, and you will notice the difference. Even my girlfriend was like, "Wow, you can see the driver's eyes...and the key hole on the door...and it's not just a silver dot, like you can actually see the hole!" I'm pretty sure that's the most excited she's EVER been about Gran Turismo. You have no idea how I dreamt of that moment...
Anyway, good luck! Hope this works for you.