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I have a rem. model 700 synthetic in a .243. I bought the rifle with glass for under a 900 bucks. Keeping in mind you want a high power scope, you could go off an get the 700 synthetic for around a grand. It is not a "Pretty" rifle by any means. I do however absolutly love my remington. It is simple to clean, hard to break and has been more than time proven. I will say that there are more accurate rifles out there but keep in mind that the rem. model 700 is what many sniper rifles are based from. Not to mention the more accurate ones will break the bank just to by but chances are they are in a caliber that in to freaking big for your reasons.
If you are looking to shoot 400 yards target, I think that what I am running for caliber (.243) would be a touch small, but the rifle comes in calibers from .17 HMR on up. I would go with either 30-06, .308 or even .270. The best would be 30-06 because the caliber is once again time proven (over 100 years) and with that, it has more research and more options on bullet weight then most any other caliber.
Oh and if you really want to get accurate, start reloading, I went from a 2 inch group and 100 yards to 5 shots and 1 1/2 holes at 100 yards with my good old Russian Moisin-nagant.
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