Your idea may initially sound good, but if you are going to do it and are not in a hurry, I’d suggest that you use another action other than a Savage.
Have the recoil lug pinned (if a Remington action). Spend the time and money to have the action trued, and you’ll have much better trigger and stock options out of the gate than on the Savage.
In my experience, I think it also better that you go the traditional route of having a shouldered barrel that is chambered by a reputable smith. Setting up the headspace with the barrel nut is not hard, but is certainly not as repeatable as the simplicity of a shouldered barrel. You’ll still need a barrel vise and a proper action wrench to swap barrels.
Buy a really good synthetic stock that fits you well, and you will be happier long term. Don’t just buy off the internet...find someone who owns the stock you think you want, and hold it/shoot it.
Consider that not all combinations will feed the same if you are looking at building a reliable repeater. In my experience, the straight stacking AICS mags made all but a few of my .308 based wildcats a reliable repeater in a short action Remington. IMHO, this was an additional expense that may cost as much as another rifle, but also adds complexity and weight that may not be part of your desire.
I put together 2 switch barrel rifles... one short action (.308 based) and one long acton (30-06 based). I’m a lefty, so when I was young and strong I built the short acton first...on a budget...and made my heavy barrel dream come true over time. Left Hand Remington action trued....308 barrel and .243 Ackley Improved barrel to start. McMillan A3 Stock and a Neil Jones tuned trigger and I was super happy. The feeding issues led me to the Badger AICS solution...but I’d need a custom mag to get it to feed the .22 BR barrel that I later bought (but I’m happy to shoot it as a single shot with a AICS single feeding Bob Sled...). This rifle weights about 13 lbs, which was no issue when I was young, but is now, so switch barrel #2 was begun.
My long action switch barrel was built to be carried forever. It is a long action left hand Remington 700 with a stock (but acceptably adjusted) trigger. Trued and pinned, I opted for a 25-06 barrel as my first because I had some serious neck issues and recoil did not help. With a #3 Hart and a McMillan Edge stock, the rifle weights just over 7 lbs with lightweight Talley rings and a tank of a 3x9 scope. I had planned to do a Whelan, but in all honesty I doubt I ever will...I think the largest I would go with this is .270 or 6.5-06...there is not anything I’d hunt on in North America that I couldn’t kill with that, and I’d still have the light weight that I have come to appreciate in a hunting rifle. A .220 Swift barrel is in the works for varminting, and I already know that I’ll have some feeding issues to work through to make a reliable repeater.
In the end, I really think you don’t save money making a switch barrel. If you are smart, you make one rifle that fits you like a glove that covers your bases. If I had to do it now, I’d buy 3 left hand Tikka T3’s for hunting...and probably save money (and certainly time)...but those were not options until fairly recently...
For the record, I’d built a number of Savage rifles thinking that making them switch barrel rigs would be inexpensive. I still have them, and they are very accurate, but in comparison to my other rifles, they are heavy and crude, and do not have as wide a variety of good stock and trigger options as other actions. I eventually dedicated them to 1 barrel.
Hope this helps.
MQ1