What does it mean to slug the barrel I'm not familiar with that term.
You take a soft lead oversize ball and push it through the barrel.
That imprints the lands and groves that you can then measure the lands and groves.
Its the least expensive way to check a barrel (there are gages and special machiens to do that but most gun smiths do not have that).
They should have a boro-scope that they can see the condition as well. Not something you want to do as what looks bad can be fine, you need to know what you are looking for.
Old barrel is very likely yucked up and copper is common (sometimes lead but lead id not shot a lot through these guns). It has to be removed to determine the barrel condition (though you can do the erosion test ok with it not cleaned up.
If its in poor condition they you have to decide if its a Restoration or a shooter.
Something not discussed yet is if you want it to shoot?
You want to go through the steps if you want it to shoot so that you are not wasting your money on a barrel removal and install and find out it won't.
The removal and install and head space probably costs $150 (also can ask what our local gun smith charged if you need some idea).