Oil and a rag, rubbing until no more rust comes off. Then oil and 0000 steel wool until no more rust comes off. The oil coat and leave it for a while. Maybe do this a couple times.
Being a .25-06 odds are slim it was fired with corrosive primers, so bore rust might not be bad (compared to the outside of the barrel). .25-06, besides rust, the most likely bore problem will be copper fouling. Odds are there might be some, but probably not a lot, as given the history you gave us, the rifle probably wasn't shot much.
The best copper remover I know is RB-17. Not cheap, nor easy to find, but it works great and is non toxic.
Once the bore is clean, shoot it, and see if its worth further work.
Replacing the barrel on a Mauser 98 is a job that needs the right tools, and for most of us, is better done by professionals. You can spring the action if you don't do it right, ruining it. Also, putting a barrel on is not a trivial matter, either, particularly headspacing.
IF you do decide to have the barrel replaced, I would recommend having a GOOD shop do it. The cost may seem high, considering what it will be worth (market value) when done, but then, we aren't doing this for market value, are we? Also, using a professional ensures it will be done right, and you will get more money easier than you will get another action, and this rifle can't be totally replaced because of its family history. Don't let Bubba and his bench vice and pipe wrench anywhere NEAR it!!!! Even if his work is FREE!
Its not like putting a new barrel on an AR, not even close. Find a shop that has some experience, if you do decide to go that route.
I did a number of Mausers back in the day, All the stock work, triggers, scope safeties, followers, trigger guards, etc. What I left to the pros were barrels and drilling & tapping for scope mounts & sights, and bending /replacing bolt handles.
Most of that has already been done on your rifle.
You will probably want a different trigger, BUT the stock triggers can be decent, though heavier than most would prefer. The two stage pull is something some hate, some live with, and some actually prefer. You can rework the trigger and eliminate the take up stage if you wish.
CAREFUL stoning/polishing of the engagement surfaces can make a difference, but I would not recommend it at this point (unless they are visibly rough) It's easy to do too much, and if you use a power tool, you should be seriously spanked or whipped.

Mauser tinkerer's rule #1, never "improve" anything you can't easily replace!
Good Luck, and keep us informed how it goes!