As far as you can shoot and have the bullet expand reliably, with enough energy to cause a bit of shock. I wouldnt shoot a .243win for deer, but thats becasue there are better options for me. for yourself I would keep it under 400yards like Sully 2 said. Unless you are very proficient with your rifle, then you could probably step up to 500-550. If you want to shoot farther than 400 yards (on deer) I would go bigger and put a muzzle brake
on it. The .264 dia and up are goin to do alot better with little recoil, especially if you break it.
.260 Rem unbraked would do the trick and get you out there farther.
I would do for something like a .280 rem around 12lbs and brake it, it would be a pussy cat. 6.5-.284 would be sweet in the same 12lbs'er.
I use my .243 alot and love it, for coyotes. Shot some rocks at 780 yards the other day and had a blast, but rocks and coyotes are diffrent than deer. Its a great round as long as you keep it short'ish range (for deer).
some guys rant about the best of the west guys killing elk at crazy distances with a .243win... video editing is a beatiful thing in the marketing word.