1 - I'd go with a new bike - after market parts are pricey and at the price range you are looking at I would that the buying power of a large company for buying components in bulk would make your money go farther.
2 - I stayed the same size on my bike - no problems either.
3 - at $1K you would be well advised to go with a hard tail - a sub $1K full suspension bike will be heavy and the moving parts will wear out quickly
4 - I demo'd a 29'er before building my bike and opted for the 26'er because of all the climbing in CO. I'm a smaller guy and the 29'er wheels didn't feel right for me on long climbs. The lighter 29'er wheels won't be in your budget. On the flip side, I can't really imagine buying a 26'er hardtail now a days either because of the ride quality difference.
Here's an article on sub $1000 29'ers:
http://www.bikeradar.com/mtb/gear/article/best-mountain-bikes-under-1000-30433/