Gust Learning
Interesting problem, and a few possibilities I think. Remington is probably the first choice, I have two 700's and no regrets. If I was doing it today I'd probably take a very hard look at a Savage.
Of course the Remington 40XB is a good choice. There are a few other alternatives that could fit within your guidelines. Find a used Remington 700, you would be interested in the action. Have the action trued and get a quality barrel and a new trigger, restock, etc. This would easily come in within your budget.
Another possibility is to take a look at the new Savage 12BVSS, retails at $675, should work pretty good out of the box and leaves plenty for a quality scope. The rifles now come with an improved trigger.
This is the short story and much of what I've said is echoed by folks on
http://scripts.xtremeaccuracy.com/index.cgi there's lots of good knowledge there. Tune in and ask.
good luck
jeff