Mmo
I like Marvel Mystery Oil and a brass brush for carbon removal. Cheap and effective + it smells good. I mix it 50-50 with synthetic 5W30 for a good all around light lube.
A lot of the info out there on gun lubes is very subjective, but the fact is I use the MMO and it works for me. A quart of MMO is about $3.50 and another $3.50 will get you a quart of syn 5W30.
If this isn't strong enough get some mineral spirits.
Good luck.