Like others have said, if this is for target shooting only, then get a big heavy gun with a long fat barrel and put a high quality brake on it. While the 7mmRM is a fantastic cartridge, it's going to pound you out of a sub 7lb. rifle. Look for something double that for a dedicated target gun.
What you need to do is get your needs in order first, then go looking for a gun. While I think the T3s are a fantastic platform for hunting and builds, they are not optimal for target shooting out of the box, but are for hunting.
Also if you are going to brake the gun (which you should if you have back problems), go with the 300WM as it will be like shooting a .308 or less when properly setup. For that matter, how about a braked .260. Maybe you don't need all the power of the magnums and will feel like a .223.
Oh, and read, read, read, read. When you get to the 100th tab, move to the "Ballistics & Range Report" forum below. More goodness there.
Edit (since your post posted before mine).
Since you have a .260, run it an see how well it does. If you need more, go with the magnum. Find the need before filling the void. That being said, if you just want a bigger boom.. go for it. I do.