I started with a 700 LTR in 308. I was able to get up to speed relatively quickly with everyone's extensive knowledge and helpfulness at the local matches. I realized pretty quickly I wanted a 260 though, along with tons of other accessories/upgrades (nice scope, suppressor, range finder, binos, etc).

I shoot a 260 now and couldn't be happier with the setup. That being said, starting with a factory 700 308 isn't a bad idea at all for the following reasons:
1) You can find a used rifle pretty easy for a decent price.
2) Ammo and 308 reloading components are relatively easy to find.
3) You can upgrade your setup in stages (trigger, stock, etc), as you try other shooters equipment. This is easier on the wallet (at least mentally).
4) Probably the cheapest way to get into the long range sport to see if you like it, while leaving room to grow (upgrades).
5) You can switch to a 260 with a new barrel and a trip to the gunsmith.

CWard's advice regarding attending the local matches is spot on. There is so much information you can gather from experienced shooters who are more than happy to share if you ask. You won't meet a nicer group of competitive shooters in my opinion. Don't be shy, come on out.