The 6.5 Swede is a totally fantastic round for hunting deer-sized animals. You'll see a lot of write up about how wonderful the .260 Remington and 6.5 Creedmore are for deer. These are both pretty much ballistically identical to 6.5 Swede.
120 and 140 grain 6.5's have nice high ballistic coefficients. They hold velocity well, and shoot relatively flat for a given velocity. High sectional densities mean penetration is good. And modest velocities mean bullets are not taxed to their limits, so they expand well, still hold together, and drive deeply. In all honesty, these are just about perfect for 100-250 lb animals.... And so long as shot placement is good and a proper bullet it used, the 6.5's will get it done on larger critters too.
Recoil in a typical scoped 6.5 Swede will run about 13 ft/lbs of recoil. Recoil from a 30-06, using a typical 180 at 2750, out of the same size and weight of rifle, will run about 20-22 ft lbs of recoil. In other words, the 6.5 swede offers really good killing power and decent ballistics with about half the recoil of the .30-06.
I've owned 260 Rem and love it. 6.5 Swede would be awesome too. I would have no problem owning and using a nice old 6.5 Swede on deer and caribou. However, if I was buying a new rifle, I'd be strongly tempted to look into 6.5 Creedmore..... You won't find many, if any, new rifles chambered for the Swede.
Recommending a new rifle is difficult. I don't know what your price points are.