The .260 would be a great cartridge to start with. Brownells has a magazine extension for short action Remingtons that will allow 5 at least in the magazine. The 40X is a great rifle. You just have to decide how much you want to spend. ATC matches are a mix of slow and rapid fire. One of the reasons the .223 is so popular is that the recoild recovery is so much faster than a .308 in the rapids. Take a look at ballistics and you will see that the 175 .308 kicks butt over the 80 .223 in the wind at 600 yds. So why is everyone going to smaller cartrudges? Recoil recovery. A .308 would be a good place to start, but you would be better served later with a smaller bullet with good ballistics that kicks less. .260, .243, 6X, 6.5 Grendel, 6.8 SPC and .223 are all that type. Long range, 600, 800, 900, 1000 yards is all slow fire. Recoil recovery doesn't have the level of detrimental affect on performance that it does in the rapids at 200 and 300 yards. It makes you tired, but it doesn't slow you down. That's why lots of shooters are going to stuff llike the 6.5-.284 for long range. Good balllistics, and it doesn't contiunally kick the snot out of you like a .300 Win Mag.
If it was me, I would build one from a box-stock Remington adding the goodies as I could afford them. That's what I did with both my service rifle and match rifle. Of course, if you have more money than me, and it's not hard, get the 40X and rebarrel for .260 or one of Tubbs proprietary rounds and go shooting.
Enjoy, and I hope to see you on the firing line.
Fast Ed