My own preference has always been to use the J&J gel (Amazon Basics baby oil gel is an acceptable substitute). It lasts longer, which not only keeps the chips looking good, but also keeps them from picking up dirt and grime from your players’ hands. I discovered that last part when, following the common wisdom of the time, I didn’t bother treating my white Paulson fracs, and within just two games, there was noticeable dirt and grime on them.
Anyway… generously apply the J&J gel with a Kiwi brand shoe shine applicator. You can usually find them in the grocery store. Twist the shoe shine applicator over the chip faces, ensuring that you get the gel in all the rings, hats & canes, and/or other molding. If you have some Gemaco soft white plastic shipping racks, put the oiled chips in the Gemaco racks to soak. If you don’t have any Gemaco racks, you can line some regular racks with aluminum foil and put the wet chips in there.
I always let the chips soak in the J&J gel for at least a week before wiping the excess off with bar mop towels (get them in the mega-pack cheap at Sam’s Club). The longer you let them soak, the longer the treatment will last.
DO NOT EVER put your oiled chips directly in PGI era ChipCo racks (clear, hard, and I think made from polystyrene) - not even after they’ve been wiped! The mineral oil will melt the plastic in the PGI ChipCo racks, effectively cementing the chips to the racks. Doesn’t do the racks any good, either. Don’t ask me how I know this.

The original ChipCo racks (which are an almost rubbery acrylic that will not crack or break if you drop them, and somewhat cloudy looking) are fine. Real Paulson racks (any vintage) are fine for your oiled chips, too.
Something else I’ve noticed: If you store your racked oiled chips in an acrylic birdcage, they will remain looking great a LOT longer!
Hope that helps!