For what you describe, I would say it is hard to beat a 16' Buffalo Canoe.
http://www.buffalocanoes.com" onclick="window.open(this.href);return false;
Brand spanking new, with sales tax, it might bust the top end of your range, but with a bit of searching or getting a blem from the factory you should be able to stay within that range.
Anything cheaper than a Buffalo, new, will be made out of a type of plastic that "oil cans" too easily, and/or is much heavier for a canoe of this size.
The 16' will be a "jack of all trades, master of none."
It is big enough to paddle tandem (two people). If the people are "average" size, it can carry two people plus overnight gear. For two people, a multi-day trip requires you to "pack light" to some degree. (Not "backpacker light", just don't bring the kitchen sink.)
It is small enough to paddle solo. Just sit on the FRONT seat, facing backwards. Paddled solo, you can EASILY carry enough gear for a multi-day river trip.
The hull is light enough for one man to load it on a car top, heavy enough to be tough and give years of service.
The hull design is identical to the old Blue Hole canoes; once considered "THE" whitewater canoe, the decendents of this design (like the Buffalo) are is still the primary rental boats not only on the Buffalo River, but also on Whitewater streams like the Mulberry and the Big Piney.
If you really go crazy about the sport like some of us and buy a more specialized canoe later, you'll want to keep your Buffalo Canoe for those overnight camping trips, and to loan to friends. I've got a Blue Hole Canoe that I purchased almost 30 years ago, it is still going strong.
EDIT: I should also plug another canoe company that is assembing canoes right here in Arkansas, Mohawk Canoes. They make several boats in the 16' range to choose from.
http://www.mohawkcanoes.com" onclick="window.open(this.href);return false;
I'm not plugging these Arkansas companies just because they're "home grown", I'm speaking for them because they make good canoes in the sub-$1000 range. Most of the major manufacturers like Old Town, Mad River, Esquif, etc get $1200 and up for Royalex hulls. The other sub-$1000 boats you see are typically some type of polyethelene, which is a very tough material, but more subject to "oil canning" (loss of shape, bowing up in the middle which causes canoe to handle sluggishly on the water).
If you're nervous about getting your canoe advice from the man you see in the Avatar, well, on the internet, you just never know who you're really dealing with....
