IMO, the Krieghoff 'perfect' gun oil is the all around best. I have purchased used guns with very grungy/mungy/dirty/sludgy checkering. A toothbrush and some product called "Wood for Good" really worked well in cleaning a shining the wood. I found that product (non-toxic, etc., appeared to be likely an import from France or Canada) at the CVS pharmacy of all places. It made the checkered area give up all kinds of grunge (likely body oils, skin cells, dirt etc.) so that the checkering was again crisp in appearance, clean, and the grain showed again. Took about five passes with a very old and dirty gun.
The stuff also works nicely on the rest of the gun if a wax is wanted. I avoid silicone products; silicone worked poorly for me and tended, I think, to entrap moisture!
But as a general rule, the Krieghoff oil used sparingly and then wiped over the gun with a clean patch after shooting works very, very well. And no, I don't shoot a K-gun!