480i = plain ol' regular TV
480p = enhanced definition (ED) -- AKA progressive scan DVD
720P = true HD level 1
1080i = not necessarily better than 720p
1080p = highest level of HD currently available on a TV (no TV broadcasts currently)
There are a few TV's out that support 1080p native. The best deal I know of is the Sceptre 37" LCD @ costco.com for ~$1500 + Shipping. There are also some new projection DLP units that support 1080p but I'm not a fan of projection and can't wait to replace my 65" living room projection TV.
The Xbox 360 will output up to 720p and 1080i (NOT 1080p), but your PC can output 1080p, so a TV that supports it may actually be a good thing if you plan to do a living room PC. I'm going to stab a guess that the PS3 will support 1080p output, but that doesn't necessarily mean it will be better.
Yes, the 360 gets hot. I'm sure the PS3 will too. There is no way you can get this many processor calculations without massive heat. Current technology just hasn't gotten to superconductor materials yet. My main PC literally heats my office in the winter. My 360 in the living room is closed up in an almost completely sealed cabinet. When I open it after playing for a few hours a gush of warm air comes out, but the 360 has NEVER crashed on me. I know I'm supposed to give it more ventillation, but I'm not and it's fine.
When I got my 360 on release day, I threw it in and popped in a few games to check them out. I was not stunned by the graphics (I had been absorbed in high-end PC games for about a year -- PC graphics blow the 360 away, in no uncertain terms). But for a console, it's the best I've seen. And the lack of jitters that I had been getting on the original Xbox is nice.
Now, for those confused people thinking the PS3 is going to shame the 360, yes, it may actually have some nifty hardware upgrades like the Blu-Ray (HD) DVD drive. It may also have faster processing power (although I think it's unlikely, and if it does, it won't be substantial). But keep one thing in mind. Graphics are software. The more graphics you pack into a frame, the more data is required. So, you can have the fanciest, highest capacity DVD drive on Earth, but it can still only pump out data at disgusting slow speeds. The reason PC works better is because the graphics are almost entirely loaded onto the hard drive before the game is started. Pulling off the HDD is SOOOO much faster than DVD/CD. What that means is, until consoles allow an actual HDD installation, it doesn't matter how fast your processors are, or what resolution the display supports, because game writers will be forced to scale back their graphics and amount of data so that you, the gamer, won't have to wait 3 minutes for every load between segments. That said, how long are you willing to wait for Blu-Ray's estimated 50 GB peak data capacity, to load from the snail-speed DVD drive? Me, personally, I don't even want them to pack more data on that disk. I hate waiting.