I don't think you'd really want to do too much at this point. A big part of the beauty of this rifle is its originality.
What I would do would be to stop the active rust, and put a bit of finish type oil on the wood.
For the rust, I would first try to remove the iron parts; The lock, trigger guard, trigger plate, butt plate, barrel. Put some WD 40 or something similar to help the screws to turn. Put it under the screw heads and on the thread ends, like on the lock plate. And no, a small bit of WD 40 won't hurt the wood, and it will help to be able to turn the screw without messing up the slot. Use a firearms type screw driver with parallel blade sides and not a common tapered screw driver. After the Wd 40 has soaked for say half a day, pick the best correct size screw driver bit, support the rifle well, put the bit in the screw slot and rap it with a hammer a few times. Then try to unscrew the screw. If no, give it a bit more WD 40 and a couple more hours. If it just doesn't want to come loose, get a helper to hold the rifle solidly. Take the gun smith screw driver bit, and clamp it in a pair of vice grips, with the end of the bit standing a bit proud of the vice grip jaws. Put the driver end in the screw slot, and tap the end of the driver bit with a hammer while you try to turn the screw out. This usually works, not always, but usually. If the dang screw won't come out, just leave it. You can still do a half decent clean up job with the parts in place. If you do get the screws out, set them in place so you'll know exactly which screw came out of what hole!
For the active rust, some fairly fine steel wool and some oil will do the job. It's messy. If you have the part off, cover it with oil and rub it with the steel wool. You're not trying to remove the solid rust, just the loose stuff, and just as much let the oil soak into the rust to slow down/stop the rusting. This is something you can do several times over a week or so. On the interior of the lock and triggers you can be a lot more vigorous and remove the rust that building up in there, so you'll have a chance of getting the lock and triggers to operate correctly again.
For the wood, some of this stuff,
https://www.midwayusa.com/product/1006518673?pid=879307 will help a lot. It just takes a drop or two, rubbed into the wood to get a better look. If you put too much, it'll tend to get shinny as it dries. If so, just buff it with a brush and take off the shine. It takes a while to dry, so go slow and take your time.
Or if you don't want to go to all the work, send it to me and I'll do it for you!
John