Remington 700s have a great reputation. One thing to maybe think about would be getting a fairly standard-issue Remington 700 sporter. Here's what I'm thinking:
It sounds like you're getting into the more precision side of shooting for the first time; and a decent Remington will outshoot you for quite a while and do everything you need it to do, but it won't break the bank. That might be all the rifle you'll ever need, who knows? By the time you get to the point where you've surpassed the accuracy of the rifle, very likely you'll have figured out exactly what you like and don't like about the rifle, and you can make changes accordingly. Maybe you'll want a shorter barrel. Maybe you'll want a match-grade heavy barrel. Maybe you'll wish you had a super-duper tacticool stock that's adjustable for length of pull, cheek height, and penis size. You can then upgrade accordingly, because you've got a solid action to build a rifle around. That's what I'd do; but that's also provided my assumption that you're new to precision shooting is correct. YMMV.