If it turns out to be pre war I would only send it to Les at Diamond Gunsmithing and have it totally restored by him.
Instead of Cerakote if you are planning on waterfowl and rough use and feel that you have to have the extra protection then do it right and send it to Robar. Black Oxide on the outside and NP3 on the internals. But a coat of good wax on a blued bbl. does just fine too and helps cut down on glare. But I don't find that a problem just don't move in the blind until your ready to shoot.
I shoot Bismuth when I have to use non tox not that much more than premium steel and the new Biz is a lot better than any steel. What constriction to open it up to for upland depends on using a flusher or pointer and bird species. And pen raised phesants an IC choke is fine. In SD with a flusher not so much. In fact I leave the 16 behind and use the Ohio 12 ga. Ultralight with a flusher there.
I do have a 16 that I sent to Briley for chokes if you want to shoot steel make sure you order the steel chokes, they have lead only also. And specify constriction not SK, Mod, etc. That way they are matched to your bbl. with exact size that you want for what ever your shooting. But going with fixed chokes gives you even more reason to purchase more guns
Not sure if you are referring to a straight tung oil finish or modified. If straight tung oil and you have never done it before I would suggest that there are a lot better finishes out there.
For modified tung oil one of the processes I used to use is the Benmatte tung oil sand in filler and Waterlox sand in top coat. It is a very durable finish and you can make it low gloss if you want.
My last gun I did went with IthacaMatts recommendation of Herter's French Red Stock Filler from Brownells and couldn't be more pleased. The man knows what he is talking about and I used to hate all stains and dyes for woodworking. I top coated with about a dozen sanded in coats of minwax antique oil finish and so far it has been as reliable as the Benmatte\Waterlox finish. It has worked well in the rain and snow for me so far.
Which became my go to grouse gun, 1949 16 ga. IC.