For a beginner you can pretty much scratch out the idea of using a cross bike in mountain bike races. The only exception might be the cross check with some very large tires on a not-very technical course. Don't get me wrong, I love riding my cross bike on singletrack, but that doesn't mean it's the right tool for XC racing.
The cross-check will be just fine for group rides, but you may find it pretty limiting in terms of a road race bike. It's not even really
geared towards cyclocross racing in many ways, though I should note that plenty of people do race on it successfully, many of whom are much faster than me
A nice aluminum cross bike will, however, do quite well as a road race bike. It's my plan for this spring. If you want to race on the road, you want brifters, not bar end shifters, and aluminum will save some weight. Obviously you want skinnier tires too, but that's a quick change. You can always try out mountain bike racing on your singlespeed. With 1000 dollars to spend, I would look at the Redline Cinquest. It's the cheapest cross bike I know of that is truly race oriented, whereas bike like the cross check, Volpe, and Kona Jake are more of all rounders (again, I've seen all of these raced in cross, but I don't think they would be great road racers).
The Jamis Nova Pro (new for 08) would also be worth looking at. Similar parts to the Redline, but it has a carbon fork and seatstays. It's 1100 dollars.