Lots of good advice. I use milcom tw25b grease on rails and barrel, milcom mc2500 oil for all else. Solvent wise to clean inside of barrel only I use the old school hoppes(not the newer elite variation, have read it causes rusting if left in barrel overnight). For cleaning I use safariland clp in the few areas regular oil doesn't wipe away crud(breach face, locking lug area).
I don't ever use any straight cleaner or solvent to clean areas that cannot be relubed(pins, recessed areas). You'll never be able to get the solvent completely out without full tear down, compressed air or not.
RM
P.S. I get my lube at Williams Arms in port perry, Ontario. They take phone orders.