Savage 11 in .260, 7mm-08, or .308 (I prefer the 7mm-08, btw) with a Bushnell 3200 Elite 10x fixed mil-reticle on top and Leupold rings. Plus, of course, bipods and a few rounds on top. While I wouldn't want to be limited to the fixed 10 power on hot hazy days when I'm hunting (wouldn't be comfortable with killing large game clean at 800 yards anyway, and I'm a confident shooter), you should find that it'll be fine for the range. As a matter of fact, the range will show you exactly what haze can do to your shooting and you'll appreciate better glass when you get it (though the best glass in the world can't eliminate haze, just make it a little easier to shoot in). I recommend this scope because it's about as good of a deal as can be found for solid optics (target turrets, 10x, mil reticle, bullet proof, capable of .5moa accurate, turrets adjust accurately as they should, and can be had for $230ish).
There are other choices. This is not the be-all-end-all. I have a rifle that is capable of hitting 8" plates every time at 800 yards that cost less than your price range. It's a Savage and I started with the Bushnell scope I mentioned (have upgraded glass since, but I still have nothing bad to say about the scope for the price). With the basic Savage hunter series you will have a sporter contoured barrel. It will still likely be accurate, but if you shoot 10 shots back-to-back you might see some drift. For caliber... eh it's on you. If reloading is an option then I would look at the .260 or 7mm-08. If reloading is not an option, then obviously .308.