If you want cheaper ammo, then run with .270 win or .30-'06.
But the 7mm remmag and .280 rem would be good choices, too, though definitely more expensive than .270 or .30-06. Of those 2, if you don't handload, go with the 7mm remmag.
But the most affordable long range round is the .30-'06 springfield. You'll have quite a bit of drop at 400 yards, so you'll have to practice a fair amount, and making a cheat sheet for your trajectory and slappibg it on the side of your rifle wouldn't hurt.
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