Anyway to answer your question. I'd recommend the 360! It has bugs but have been worked out by now. The PS3 also has bugs but cost significantly more. Don't waste your time/money on the Wii. That is some hard shit to learn. Graphics are childish and to much damn moving around for my likes!
High definition isnt the important thing to take note of, here. What's important is the game and the texture resolution (size = bigger is better = not blocky/blurry like when you walked RIGHT up to the wall in doom1 or Goldeneye N64 = you can walk up and see the hairline fracture in the cement wall with a 2048x2048 texture plopped on a small wall)
So it goes something like this: Just because you have a high definition TV doesnt mean every channel is going to come thru in hi-def. The same is true of the PS3. Just because everything can come in clearly at 1080p doesnt mean the walls, guns, or people's faces will be to yours.. or anybody's liking as far as detail and clarity go.
But.. to answer your question.. yes, the PS3 itself is HD-ready. Whether the games will use that resolution or not.. is entirely dependent on the manufacturer. It's a huge tradeoff, frankly. Do you want to put all the processing power into the 1080p res with antialiasing and try for consistent 60 FPS? But then we might have to trade off physics details, level-of-detail will only be at short range..
(example being the mipmapping/blurring the ground, walls and player skins once youre at said distance away from it. Goldeneye the sample, btw.. walk up to a wall, stare at the ground and notice the different levels of blur/mipmapping as you walk backwards. That process halves, or cuts the texture's size to save video memory in the game. Plus.. at lower resolutions it can produce an interesting, pseudo-moire effect. Moire being the rainbowy.. zigzagging effect on extreme details without extreme representation on your screen. Many people dont even know it exists until.. yup, until they actually LOOK for it. Like deinterlacing or.. geez, anything on TV.. or related to video output. Whew.)
.. so anyway, you cant have it ALL ways. Smooth framerates, overall screen resolution, physics detail, LOD, Antialiasing, draw distance and what kind of filtering should we apply to the textures coupled with the possible shadow/lighting detail being the primary concerns.
btw, Goldeneye ran at 512x384 with x2 AA and bilinear filtering on the custom SGI setup on the 64. But the N64 never sold a VGA output anyway.. as I recall. Which would be really easy to do, as most consoles actually put out the pure signal and the only real conversion is to NTSC/PAL. But.. yeah, the first was the VGA cord for dreamcast. But not all games supported it. Complete piss, that.