Oh, man, I shoulda looked more closely at what you had.. Savage 3's were made from 1933-1952 and were Very Simple rifles. You lucky dog
26" barrel on Pre-WW2 & 24" barrel on post WW2 rifles.
Ok, you have a few choices here...it is an old rifle, but not a very Monetarily Valuable one...meaning that if the stock is messed up it wouldn't hurt to put a new one on it, or to refinish it...or replace parts...etc.
If it does NOT have a front swivel for a sling, you may decide to drill & tap to put one on it so that you can put a Rock Mount Bipod ($39.95 @ Walmart) on with no headaches...it will only enhance the utility and value of the rifle. Or if you can find a bipod in an old gun shop that is more the age of your Savage, even better. But since the Rock Mount is adjustable, it'll help accuracy more.
When you build the new stock, remember to drill & tap for swivel sling attachment points as well...makes putting extras on a little easier. Not to mention having a sling to use as a tensioner also helps accuracy as well.
As far as the Trigger goes, yeah, take a few pics and post the clearest ones

You may not be able to do more than polish it a bit...depending on how it is made. The Gunsmith Forum on here might be your best bet there...lotsa old guys who have hopefully worked on Savage 3's or similar rifles in the past