Right, it's mostly the amount of space on the hard drive. I'd say the best one that you can easily find is the Elite. You probably will have a hard time (if it's even possible) to find just an Elite, because most or all of them are purchased with a game and is specialized for that game. For example, I bought my Elite with Final Fantasy XIII and on the top of the xbox is a metal plaque that says 'Final Fantasy XIII.' Haha, it's really cool.
I don't know what you mean about the HD being big, but the TV plays a lot into HD and stuff. I have a TV where motion shows up better or something, so yeah, a lot of it is about the TV not the xbox.
I would also recommend you get one of the new black Xbox Elites. They have an extra fan, which will keep your xbox cooler and prevent more freezes. They also run more quietly.
To conclude, my recommendation is the black Xbox Elite. Plenty of space and it runs better. I would also suggest you get something like a grate to put your xbox on. It should be elevated (so it's not touching the table/floor) and have air space in it. That gets your xbox more air and less dust which can collect inside. Good luck!
PS: The black Elite is also really cool because you don't need to click any buttons on it; they activate upon touch! :D