I think you're on the right track with the Savage. In fact, I'm going to buy a 14 American Classic later this month in .243. It's very, very hard to better in the trigger department than the Accutrigger.
If you're still open to suggestions, another fantastic rifle is the Tikka. This rifle is made in Finland by the esteemed Finnish rifle maker Sako and for out of the box accuracy and a durable design, they are tough to beat. The cost is almost exactly the same as the Savage, which technically makes them even better because they share many of Sako's design attributes, but they come at about half the price of a Sako.
As far as your cartridge choices, a couple of thoughts.
I'm a handloader and the .270 WSM is one of those "short" cartridges like the .243 WSSM that doesn't offer a whole lot of advantages over its "long" cousin other than the shorter bolt action, of course.
As a tradeoff, you're sacrificing a lot in terms of off-the-shelf ammo selection and WSM ammo almost always sells at a significant premium. It wouldn't be unheard of to spend $25 or more per box for WSM ammo. I don't know about you, but when I get a new rifle I want to shoot it and I personally don't feel prepared unless I shoot at least a box of ammo before each season. That could run up quite a tab with the WSM.
There's nothing wrong with a .308, but have you considered a .30-06? Ballistically, they're fairly close, but with a slight edge to the 06. In terms of ammo selection, however, the 06 beats everything hands down. You can get everything you'd ever want off the shelf in .30-06 and for your needs I think it's worth considering.
Welcom and good luck.
Grouse