Some, myself included, might suggest a slightly lower rifle budget and a slightly higher optics budget.
My heavy 243 is a Winchester Coyote. It is one of the two rifles I shoot the most. In this picture, it has a Swarovski 6x42 scope but it now wears a Zeiss VM series scope 2.5-10x50. You probably don't have to get that high end of a scope but I think a rifle in the $550-$650 range would be very suitable and that would allow another $250-$350 for a better scope. Unless you happen across a used Sako for $850 or less that you like, then I'd probably go with that.
I like Rugers and Winchesters so that is what I would recommend. Winchester's Coyote model and Ruger's VT series rifles have laminated wood scopes while many prefer a synthetic stock. Ruger offers their 700VS in 243 and I wouldn't recommend against it, just as I said, I prefer Rugers and Winchesters. Any of these should run you $600-$650 or there abouts brand new. If you're not inclined to tinker with such things, you'll probably want to have a trigger job done to the rifle and this can run anywhere from $35 to $80 and would be money well spent esp when you get to shooting at longer ranges. The two things that might increase accuracy would be to have the barrel crowned and have the barrel set back some distance. You won't know until you see how the gun shoots and which loads are best in your particular rifle. Having said that, most guns these days are very accurate - more than likely more accurate than you will be for some time. no offense.
For scopes, I'm a bit fan of the Weaver Grand Slams but the Nikon Monarch and Leupold VariX II or III are viable certainly options. I would probably suggest that you won't need as much magnification as you might be inclined to want. I almost always use 6x setting on my variables and I've seen some guys do some might fancy shooting with 6x and 10x scopes. You don't need a 24x capable scope for shooting at 600 yards and your money would probably be better spent on a higher quality but lower magnification scope. A 3-10, 3-12, 4.5-14 or so should do you just fine for a long long time.
SWFA has a used optics list that can be seen
here that usually offers some very good deals and some great deals from time to time but you have to watch closely as the good deals go pretty quickly.
Good luck and certainly ask more questions.
