Thats a tough one, but if you are serious about the restorla its worth a chance for the $50 and then take the following steps.
As a first step: There are gauges that check muzzle and trhoat condtion. I can't remember the name but can get them for you if you want.
If you can't get the barrel checked with the gauges before (unlikely), then you can find a gunsmith that has the gauges when you get it. Those check the throat and muzzle for erosion. My brother has a set as he is into 03s. I forget what they are called. It gives you an idea of what condtion both ends are in before you commit to the barrel change.
The more critical one is the muzzle, a 2 or 3 is great, 4 ok and I think 5-6 is iffy. Anything past that is toast (that's off my head so those could be wrong, go by the details). Throat erosion is not so bad as that has far less affect but it does tell you a lot about how much it was shot.
You can also have or you can do it yourself, slug the barrel to see what the land and groves look like.
As for cleaning it up, there are a lot of copper cleaners (the usual culprit). Outers actually makes a kit that does it by electrolysis (for around $100). You do want a clean barrel and its a lot easier to do it before its on the gun than after.
You would need to find a good gunsmtih if you are going to do this and that's the other part. Get referral from him (or get them from friends). Make sure he has done a number of 1903s and they are happy.
A good 1903 smith will have the gauges, head space gauges and can slug the barrel as well.
The 1903 is not the worst but its not an easy one to do, so the guy has to know what he is doing with a 1903, not a Mauser.