Stopping any further spread of rust is priority, light oiling and a wipe down whilst trying to preserve the patina is important to me my 1916 303 was a good learning curve with a brought over the phone for $100 some 18 years ago yep all there she's good to go faaark me dead not even close when I picked it up what a sorry ar*ed sight but basically intact cost nearly 9 times its price to get it to where I wanted it. (I discovered it was a 5 MD thats why I took it)
There are those that seem to think highly polished oilers and shell cases are the go they are not they were only ever shiny when brand new even then shiny stuff is just what an enemy is looking for as dirt and trees are not shiny unless wet!
Anyway me I do try and preserve as much of the patina as possible without it looking like its to go out on a parade ground for inspection by the OIC.
Cleaning a stock from crud build up and oiling it up is mandatory but you dont have to go over board with the unissued look if its clean to handle and oiled properly they look good, all my shooters are just oiled up I dug allot of crap out of the hand guard flutes on the 4's all had a light rub over with 0000 steel wool then oiled and there you go they look good.
My 1920 Lithgow's fore wood and top guards are in the white and never been sanded down from the time they were replaced, were they replaced in service I don't know did a gunsmith replace them I don't know I have just left them as is and done as above and left them its part of that's rifles story why should I change it a 99 year old rifles appearance just to suit some one else's view.
A pic taken a few years ago of my meagre 303 collection top - bottom 1916 5MD Lithgow MkIII, 1920 Lithgow MkIII, 1945 MA MKIII, 2 x 1942 Savage No.4's, All original 1944 M47C No.4 T with its original MkIII 32 scope.
All they have all had was a little stainless steel wool & WD40 on the odd rust spot and BLO/Turps mix after a light rub down with 0000 steel wool (The wood parts only) then just wiped down re-oiling every now and then.