What are some things I should know about for the 360?

IE, preventing overheating or drive damage...

Is playing the console horizontal and after turning it off putting it vertical to allow cooling of underside a good idea?

I can only provide you with some basic tips:

1. Clean dirt and other nasty stuff from your 360, especially if it's near the vents.

2. Keep it away from your carpet or floor. A table should do fine.

3. When closing the disc drive, press the button next to the drive instead of pushing the drive closed with your hand.

4. Don't rest anything on your 360, especially food/drinks. It can be tempting, but don't do it.

5. Make sure the room is well ventilated/cool.

According to my friend who works in Currys in the UK, since they have been selling the Falcon model they have only had 1 returned that had a problem. Thats since December 2007.

If you have Falcon just keep it ventilated and you should be fine.

idk...my cats have laid on my 360 (while im playing even) and ive not had an issue so far.   i wouldnt let the big fat one lay on it, but the smaller 2 i have.

One thing I think you can't underestimate is the power of keeping the room itself clean.

1. Clean your ceiling fan off at least once a week with some cleaner and a rag(I like microfiber)

2. Lightly vacuum your room daily and at the end of the week give a thorough run over with it.

3. A good air purifier that does not release ozone as a by product. You can also use one of those newer "air sanitizers" that incinerates virus' and such too if you like.

4. Dust about once a week and leave a window open at least a little bit every day to let excess dust flow out.

A little excessive but if you follow this you'll find your room and by extension everything in it a lot less dusty.

Just make sure the heat can get away from your 360. That is pretty much about it.

Can't keep it on the carpet?

The only other objects I can easily move there easily is a leather stool or just a plain plastic stool...

Will those suffice?

Carpet will help lock heat in the system, potentially clog up the air vents and a lot more dust will be kicked up by the cooling fans and get into your system.

What I do is keep it up off the ground in an unenclosed area (not inside an entertainment cabinet) and I try not to leave the thing running all day.

I always hear different things about vertical vs. horizontal. I finally settled on horizontal. It seems like then at least all the vents are open. If you put it in a vertical position, you're actually blocking one vent. I also stick with horizontal because it's less likely to scratch a disc. I have never had any scratching issues, noise issues, or overheating issues with my 360 (Falcon), but I don't want to start having them, so that's what I stick with. I keep my 360 on very open and well ventilated tempered glass shelf on my entertainment center. That way there's no carpet to collect heat and static.

How openly ventilated should I have it, because I am tempted to put it ontop of my TV (a CRT tv), instead of a small table that I have to the side of it (I want that for my laptop!).
I have been careful to avoid putting consoles on my carpet recently, and I have realised that might be why my first PS3 broke, and a PS2 broke (they were disc read error stuff)