I have been looking for a .22lr single shot and the old Stevens have caught my eye. Ones with bad barrels are very reasonably priced.

Has anyone here ever gotten one rebarreled and can speak to the difficulty and expense of this?

Thanks

You might consider having it relined. It's cheaper than rebarreling and it retains original contour and factory markings.
Be sure though the barrel is bad and not just very dirty due to never being cleaned.

I never thought about lining a barrel. How does that work with the extractor cut out?

Relining is a practical way to bring these back to life IF you have the tools. The extractor cut will have to be recut in the liner face. Frank de Haas' book on "Mr. Single Shots Book of Projects" tells/shows how, I think, if you can find a copy. Numrich's used to sell already chambered liners.

They also used to sell replacement barrels for Favorites, so you should have a look and see if they still have any.

My first rifle was one of these that dad got relined. The extractor wore out though. I was told it couldn't be fixed.

NOTHING on a Favorite can't be fixed. Just a matter of money and/or time/skill. They are very simple firearms; many functioned with firing pins made from common finish nails for years. Extractors should be available or if you have the pieces of the original, you can silver solder them together. One of the modern adhesives might even work if you don't savvy solder.