I have used an old Silicone Gun Cloth for years for wiping down the steel and wood. Protects against moisture / fingerprints etc. As my cloth has got a little more "tired" over the years, I augment this with a small drop of Abbey Silicone Gun Oil 35. I've owned some of my rifles for about 45 years now and, despite extensive field use when I was younger, they still look superb now.
You just don't want to let silicone get on any metal to metal contact surfaces.
I've recently also bought some Ballistol oil to try. I've only ever heard good things about this.
Our sponsor, JS Ramsbottom, is a fantastic, easy source for the above and many more gun care and airgun related products. Always competitively priced and offering brilliant service.
P.S.....And a very warm welcome to the forum.