Affordable is a loaded question. For competition, I see affordable as $5,000 or less. Do you? If so, the 6x47 Lapua is a great choice. You can shoot up to 115 grain bullet, and as light as a 65 grain. I have one that is a shooter out to 1000 yards, as do several of my buddies. The 6mm gives you a very stable bullet, and for accuracy the 105 gr A max is incredible.
This is a wild cat round, so you will need to get one from a Custom shop. Mine came from SSG, but there are several very reputable builders on this site. Dan Glover, of Dan's Custom Guns has built a few awesome guns for friends of mine, and a tremendous 7x300 WSM for my dad. When a 72 year old man can stack bullets on top of each other at 500 yards, you know the gun is a shooter.
Next, just because you have the gun, you better have good tracking glass, and have it level. The gun means nothing if you can't see or dope in your target. If you are talking competition, get your press and dies and a good powder meter and calipers. Don't go cheap, you are going to end up with the good stuff anyway, so save yourself the trouble.
Then shoot, and shoot some more. Find a load, chrono it, and use it. Dial it in, make a drop chart, then buy a nice range finder. After 400 yards, most loads are falling pretty fast and you need to be correct on your yardage to dope the scope correctly.
Get a good bi-pod and rear bag and you are set...
Enjoy.
Roger