My 7mm-08 is a Browning A-Bolt, and while I love it I would not list it as my first recommendation, simply because mine HATES all factory ammo, shoots ghastly 5" groups at 100 with every kind I have tried, but shoots cloverleafs with my H380 and Big Game handloads using Sierra Game King and Pro Hunter bullets.
If I were to purchase another 7mm-08 I would go for another Tikka if I wanted synthetic or a Winchester 70 Featherweight if I wanted blued/walnut. Both of those rifles have performed very well with factory and handloads and are a delight to shoot, well designed and well built. I would not hesitate too hard on getting another Savage either, but much like the Browning they sometimes don't like factory much either (1.5-2.5MOA). I have had half a dozen of them they are hit and miss in that regard, but all have performed very well with SGK or TTSX handloads.
Edit: I would be very hesitant to try another Remington after that last disaster they called a rifle. Yeah that was 2008 but it still pisses me off they would let QC slip that far. I expected much better from the legendary Remington 700, my other older ones were MUCH better even with their flaws.
The 6.5x55 is another great low recoil hunting round, similar to the 7mm-08 and my personal favorite hunting cartridge, but it is something of a handloaders cartridge, since some 6.5x55s are over 120 years old factory ammo is loaded to a VERY low pressure and will not give good 300+yd performance, you can safely stroke another 300-400fps out of it if you roll your own and that puts it in the same class as the 7mm-08, slightly smaller caliber but considerably better downrange ballistics, if you wanted a 6.5mm and did not handload I would opt for the Creedmore or the 260 Rem they are made for modern pressures (62,000 psi+)