Is the barrel stainless steel or just plated with something?
If it's stainless steel, just leave if bare.
If it's plated steel, you could have the plating stripped and just leave it bare. MOST automatic pistols still have bare steel barrels, and no one seems to have much trouble as long as you do normal maintenance.
If it's plated, you may have to have the plating stripped before you can have some finishes applied.
Normally, it's extremely difficult to get every trace of plating off using home methods. It may look like it's all off until you apply a chemical finish, and you see what looks like white freckles. That's remaining plating that prevents a chemical finish from adhering.
A good all around finish is to have the barrel hard chrome plated, which is what may be on it now if it's not real stainless steel.
Most of the hard chrome re-finishers offer special prices for loose parts like a barrel.
If it's already plated with something you will have to have the refinisher electro-strip the plating off before most any other finish can be applied.
Recommended gun refinishers who do hard chrome are APW/Cogan, Ford's, Armoloy, Metaloy, Techplate Inc.
The "paint" type finishes like cerakote, will scrape off a barrel, and finishes like TiN etc are expensive and hard to find a gun refinisher who offers it.