There are two different size lock nuts on the Savage rifles and the wrench that will take care of them will come with many new barrels as a kit. You can also order barrels all contoured, threaded and chamber cut through places like Brownells and Shillen. The only issue is if you want the barrel drilled for iron sights. The beauty of the Savage is that you can adjust headspace with a turn of the barrel and tightening the lock nut.
Some kits will also include a chamber gauge (usually a field gauge), IMO these are usually on the lower end of quality. If you decide to change out the barrel on a savage yourself, you may decide to do it again so just buy a wrench for about $30 sometimes less on Ebay as some people buy kits and sell the wrenches when done their project (think I paid $20 for a used one).
You can also rent many of the tools including reamers which if you get a short chambered barrel with sights on it you will need and also a set of Go-No Go gauges from several companies, a couple I'll put links to below.Or of course you can check with a local gunsmith and see what they will charge to do the change over for you. If you are not mechanically inclined and plan this to be a one and done project I would suggest using a gunsmith.
https://4drentals.com/ offers some good info on which barrel you need and you can rent the gauges for under $10.
https://www.reamerrentals.com/ Again a wealth of good info and they rent their gauges for about $7