I would go for the XBox 360s. It is the most desired moel and since it is sandwiched between two other models, could be hard to find.
If you get the original phat 360, as long as it works you should be fine. But clean the system when you get it. Most people think that the systems are crap, but tend to be the same people who never clean their computers of dust. It's just something you have to do. And with modern systems being PCs, clean them. This video is a good one:
I'm running a really old 360 and have zero problems, I just keep it clean.
The tray doors tend to have to have their belts cleaned. Most of the time, you don't have to replace them. I never have. But I have cleaned gunk and applied a tiny tiny amount of grease. There's videos for that as well. This is standard maintenance on ANY modern disc based system.
But honestly, if the system works, you should be fine. Just stay away from any advice with towel in the title. Unfortunately Douglas Adams was before the 360.