Before you do anything, you need to do an inspection of the barrel. I'd slug it and look very closely at the rifling. No point fiddling with a rifle with a poor barrel.
Restoring any milsurp has gotten really expensive. It's mostly about all the wee metal bits. Gunparts, for example, wants $5.50US each for a large butt plate screw. $12.50 for the lower band assembly(front sling swivel to the rest of us). $207.50USD for a new walnut repro stock with no metal. $32.75 to $40.75 for a new lower hand guard and $26.00 for the other one. Nearly $300 before shipping and all the metal bits. They do not have any original surplus stocks. And a lot of the wee, tiny, metal bits(screws and such) they don't have at all.
However, since your current plan is to build another sporter on the 100 year old action, don't even think about a military style stock and all the wee metal bits. No need to inspect or slug the current barrel if you're going to change it anyway. You will not be keeping it remotely "correct" with your 'current plan' though. Not a big deal though. It has no collector value anyway.
"...barrel should be free-floating..." Floating a barrel guarantees absolutely nothing. Some rifles like it. Some do not.