Buy your self a Remington 700 Sendero in 300 Ultra Mag, They offer power level ammo 1-3 One level is .308 level two is 30-06 and level three is 300 ultramag All from the same case it is perfect for the guy just getting started that dose not reload as of yet, you have the best of all three worlds to play with, now put a nice Leupold on top and a set of Harris bipods underneath it, Get a good wind meter and a good spoting scope along with a good range finder and you are set to see if this is your thing or not for around 2,200 to 2,500 not including ammo. If you find you wan't to persue this hobby then move on to spend the big bucks.
Remember to purchace ammo by the case to get the same lot numbers so you keep everything consistant.
Truth be known the .308 runs out of ass at around 700-800 yards the 30-06 is still in the ball park at 1,000 yards and the 300 Ultra Mag will stop a cement truck at better than a 1,000 yards, just depends on your perticular application.
To become a great 1,000 plus yard shooter requires thousands of houres and tons of money and in my case my first wife!!! she just didn't understand. and a love of math, that and alond with a stedy hand good breathing you should start seeing improvement each visit to the range, trust me if you are not patient this is not what you should be setting your sites on.
I wish you the best of luck, If I can be of any ferther help please feel free to message me.