Saad- You have a very nice shotgun.
Here is my rule for restoration work.
First, Do no harm.
Others have already suggested on what to do with the barrels.
Here are my unsolicited remarks concerning the woodwork.
It took 100 years to get the patina on that stock. Clean it gently, maybe steam out a deeper dent, but mostly, Leave it alone.
100 years of use put a lot of stories in that stock. Enjoy them when you look at it. You may, after cleaning it, desire to rub/buff it a little with a soft cloth. Maybe a little paste wax. Not much else. It looks well maintained. Don't spoil that.
Scrubbing the rust off (as previously described) is of course, just good maintainence.
Remember, first do no harm.
Just my 2 cents.