Savages are easy enough, I did it myself. Watch youtube, it will show you how to do barrel swaps. Lots of discussion on headspacing (whether you need a headspace gage or a piece of brass. Since this is your first time, do it right and get a gage.) You will need a barrel vise, action wrench and barrel nut. I have done it with out the action wrench, but it makes it easier to remove the barrel with one.
All of these recommendations are assuming you are on a budget. I agree the 308 or 6.5 cartridges are the way to go. I'm partial to the 260 rem, but component and ammo is a bit tougher to find than 308.
Boyds has about the least expensive stocks I have seen. 100 bucks shipped, but you will have to bed it your self. Again, youtube is your friend.
Gunshack has the least expensive barrels (ER shaw, I had one that I shot some pretty small groups with and would buy one again), but if you want a bit higher quality, go with a criterion barrel from Northland shooter supply.
Read up on OCW load development. Dan Newberry has a website that explains it better than I can ever do. Look that up and read it.
Optics, if you are shooting it now you probably have optics. If you decide to upgrade look to a fixed 10X SWFA or bushnell or weaver. All are solid performers.
Going through the budget build process taught me a lot about my rifle and it capabilities. You will have a fun time with this.
Sean
