Bit of both
Savage 110/Steven's 200 Yes.
Edge, not so much. The Edge is new and there is virtually nothing available to allow customization. That may change.
Savage barrels are pretty good. Unless you want to do long range target work I'd stick with the one you've got. Most people tinker with the 110 series to give them multiple caliber capability off the same reciever. You can switch a savage barrel in about ten minutes to another caliber in the same family(say .30-06 to .25-06, or .308 winch to .243 winch).
Accuracy wise the 110 platform can benefit from a trigger upgrade and machined recoil lug. A good trigger will run you about $100 and the lug about $30.
Many times you won't need either as savage will often shoot sub MOA out of the box.
For what you are looking for you probably would never need to do anything but sight it in. Most savage fans just like to mess with things.