There will be a host of responses to this question that endorse one practice or product over another. I like to use Hoppe #9, Rem oil, and a silicone rag to finish on the outside surface. I keep Hoppe #9 away from the outside SS finish surfaces and use Rem oil which acts as a solvent too. After cleaning, I store my firearms in a silicone treated sock in a gun safe with a Golden Rod to remove humidity.

There are plenty of online videos and experts (in their opinion) with advice. I found this article that you may find helpful: https://www.gunsamerica.com/blog/how...-your-handgun/