Do I have to worry about the case getting scratched or the paint chipping, and if so, what can be done to prevent it?

the paint won't chip unless you drop it. As for scratches it is pretty durable. If you are worrying about it buy a leather or rubber sleeve that encases the tablet. you can find them online like on ebay.

Besides the screen which I take good care of, my n800 is pretty much abused. And besides 2 scratches on it's foot (where it droped) it has no scratches and no chips.

(Older post, but I'll add to it for future readers' benefit)
The N810's front and back panels are aluminum, I believe, and are hard to scratch (at least, unless you're trying :P). The side edges are plastic, and will scratch. I dropped mine from waist-height onto concrete (>_<) and got two deep-ish scratches on the edges, but nothing else was damaged or disfigured. (I may have been lucky, though - I've since learned to unplug the earbuds before taking it out of my belt-case, as the cord tends to snag)

It's much more durable than most cell-phones.

If you're really worried about it then you can always get the invisishield full body kit from zagg. Then your entire N8X0 will be scratchproof.