My first rifle was also a Rem BDL in 243 which I used for deer hunting in PA. I liked it, however, the bolt body developed a crack in it after about 100 rounds through it. I sent it back to Rem to get repaired then gave it to my younger brother and went out and bought a S&W M1500 in 7 RM.
Since then I've owned numerous rifles including 2 Senderos which I have since sold. They were both good shooters and no troubles with them. Recently I did a 300 RUM build on a 700 action. I replaced everything except the receiver itself.... the bolt, the trigger and the recoil lug. It is a very good shooter.
That said, the 700 actions are not my favorite by any means because I feel you must replace everything to get a really good action. For lesser cartridges replacing the recoil lug isn't necessary.
My favorite factory actions are the Weatherby Vanguard/Howa M1500 and the Winchester M70. However, I would not use them for the longer cartridges such as 7 RM and up because they are a bit on the short side to reload efficiently for the longer high BC bullet in those calibers.
Which brings up another issue for you. If you buy a factory rifle in 7-08 and/or 308 Win, it will come in a short action which will stifle your reloading for long high BC bullets. This is the conundrum for LR shooting. There are very few factory rifles that are designed to efficiently use long high BC bullets in short or long action. In the case of the 700 actions you can modify them to accept COAL's of close to 4".
If I was going to go with a 308 (or 7-08), I would find a used Vanguard/Howa or M70 standard size action for as cheap a price as I could find, have it trued up and put a good match grade barrel put on it and put it in a B&C Medalist or better stock. I would rather invest in one well crafted rifle that that will do the job efficiently than buy two rifles that don't really meet my needs.
That is exactly what I did with two other recent builds for a 6-284 and 6.5 WSM. Using the Vanguard actions was much less costly than the 700 build as I did not have to replace the bolt and recoil lug (the recoil lugs on Howa and M70 action are integral in the receiver) The howa bolts are one peice and have M-16 like extractors. I put a Timney trigger in one of them and the other I stayed with the factory trigger which I was easily able to tune to a crisp 1.2 lb break. The Timney has a 3 position safety and breaks at 1.5 lbs. I can not tell the difference between the factory and Timney triggers.
Also, the twist rate in a factory rifle might be too slow for long high BC bullets.
On cartridge selection, I would go with the 308 period, for target shooting and hunting. I do not know why anyone would take a 7-08 out to the field to hunt with when they have a 308 in the closet. Makes no sense to me, no offense intended.
If I had a 308, I would be loading 215 Berger Hybrids over RL17. An excellent target and hunting round and 308's have great barrel life.
http://www.longrangehunting.com/forums/f19/ok-i-am-believer-308-rl-17-208-amax-sweet-spot-54102/
http://www.longrangehunting.com/forums/f19/215gr-berger-hybrid-308win-104197/
