It's easy to do, but don't fall into the Savage heavy barrel trap. There are a ton of pre-fits out there but most of them are heavy bull or varmint contours, that regardless of how well they shoot they are worthless on hunting rifles. So get a sporter contour at the least for a .338-06, and I sure wouldn't go heavier than a magnum contour. So your biggest issue will be waiting on Shilen to make you the tube.
Or you could just buy this rifle and have no wait:
Mauser .338-06 with dies I'm not trying to talk you out of building a Savage. They're fun to play with, its kind of late me an adult erector set. Ive built a fey myself, but in the long run there is only about $300-350 difference between it and a M700 build anymore.
You need at a minimum a barrel nut wrench and some way to hold the action or barrel. I've cut blocks of hardwood to hold the barrel and used them in a 6" vise, I have used a piece of leather to hold the action in same vise. Once in a pinch I used a large crescent wrench to hold the recoil lug to remove the barrel nut.
The barrel nut can be stupid tight so using a good penetrant like Kroil for 24 hours prior to removing the nut helps. A little bit of heat from a propane torch or goo heat gun works well too. Don't worry about buying a squared up recoil lug and barrel nut unless you're going to have a the receiver squared up as well. With the floating bolt head the factory stuff works well.
I recommend getting headspace guages, at the very least a go-guage. You can just add scotch tape to the rear of the guage to use it as a no-go. Gauges can be bought from several places, or you can rent a set from companies like 4D. I recommend buying a set of guages if you're going to swap barrels on a regular basis.
