I built something similar just recently...however haven't really got it to where I'm ready to try real long shots yet (only 21 down the tube). I went with the scope mentioned here: Best current sales on scopes
It's a pretty clear scope, really,...even at full power, which some less expensive scopes loose clarity when at full power. Just a thought and it's a little over your target price.
I've got a friend that has the Bushnell 10x40 Elite Tactical. It's a nice scope, and can be found for $200. I'd say if you really want to play at 1K yards 10 power may not be enough, and the 14X I mentioned above may be marginal as well. Hopefully others here will chime in as I'm no expert at optics an attempting 1K shots.
Let us know how your quest goes.
BTW, I've got ~$615 into my budget set up.