I'd take it apart (separate metal from wood) and work on both separately. The metal parts are best cleaned in an electric bath which will remove all the rust but not the blueing. Easy to do, all you need is a small tank where you can fit the metal parts (preferably plastic) and a 12V adapter (or almost any adapter, for that matter). There are detailed instructions on the net about this (try YouTube). Or go here:
http://www.surplusrifleforum.com/viewtopic.php?f=80&t=62728&start=0
As for the wood, clean all dirt/other stains off it and put some stuff on it to preserve it (see post above as an example). There are various options, the most basic one being oil. Personally, I've had a great result with rub on floor varnish on one of my antique rifles... after rubbing on a very small quantity of it all over the wood, it gave the stock a whole new look, without being noticeable.
If you don't want to do that kind of restoration, then just sell it. One thing's for sure, rust will just keep getting worse and eventually turn the gun into unsalvageable junk, especially if it's going to be kept in a fairly humid environment (such as a house wall). The poor thing deserves better IMHO.
By this point, a lot of what was bluing is now browning, from fine rust over time. If you put it in an electrolytic bath there will little finish left probably. If you want to get rust out of the bore, use vinegar, but first you have to get ALL the dirt, oil and grease off or the vinegar will not work. You can also get fancy preparations like this:
ht tp://www.evapo-rust.com/testimonials/testimonials.php?content=forensic_gunsmithtestimonials.html but this stuff takes off ALL THE FINISH, just like vinegar does. You end up with metal "in the white".
The bore can be done that way, but you have to be very careful to plug the nipple hole. After all the dirt, oil and grease is removed so the acetic acid in the vinegar can actually get at the rust, a week or two will suffice to convert all the rust. Then you can brush it out, or better, put it back in the ultrasonic and all the rust will blow off as black particles, right down to the bottom of the pits.
I've never heard of an electrolytic bath that doesn't take off all the finish, but I'm interested if someone else has evidence of one that doesn't take off bluing.
There is also a certain amount of cross-over between bluing and browning: "rust bluing" for example.
If you want to clean it, carefully disassemble it and have the parts cleaned ultrasonically. A blind cleaner size machine will do the barrel and breech together. Trouble is, the wrong solution or leave it in too long and you'll have etching and loss of finish.
I would put the metal to soak in penetrating oil for a month or two and then using a piece of brass, carefully scrape off the superficial rust. Gentle use of very fine steel wool, always in straight lines can help too.
There is no quick and easy method and it's very easy to get carried away and do too much: steel wooling the stock for example, which will ruin the patina.
That's why I suggest you leave it alone. With a bit of preservation, you can have a fine looking wall hanger that will not deteriorate any further. In fact regular oilings will soften the rust and improve the wood, so that future cleaning will be easier and more effective.