How do you clean and protect a non chrome lined barrel? for maintenance and long term storage?

Hell I'm curious. What kinda stick have you purchased there tiger?

I used to have a SBR with a non chomelined barrel for HD  which was rarely shot. What I did was coat the outside of the barrel with clp and the bore with Mobil 1. Always do a pms every 3 months and repeat oiling if necessary. Clean routinely as usual.

For all of my shotguns, rifles and handguns, I lube the bores, cylinders and slides with RIG Grease.  RIG is now made by Birchwood Casey, but it has been around for many years.  In 50 years of shooting, I've never had a spec of rust show where it has been used and some of my guns have gone years before being used.  Apply RIG liberally to a patch and coat the barrel, chamber, bolt and carrier.

The one attribute of grease is that, once applied, it stays put.  Gravity causes oil to migrate over time and so it's not the greatest for long term storage.  RIG can be removed with a bit of solvent on a rag and I usually use several patches wetted with Coleman Camp Fuel or Lighter fluid pushed through the barrel and chamber to remove all traces of it before firing.  

To be sure, there are other products that will give you good results.  This one works for me.