I have the Tipton vise at the cleaning table in my shop (not the "newest" one, it's crap).
Amazon product ASIN B09776FTDW
You want a quality, ball bearing, one-piece cleaning rod (Dewey)- either steel, or plastic coated
No jointed, sectional cleaning rods, they'll flex and contact/scrape the bore. No aluminum/brass- too soft, they'll pick up crud and scrape the bore.
I prefer the vinyl coated- but they need to be inspected to be sure nothing gets embedded that can be scratch the bore.
Bore guide for your action type(s).
For field use, bore snake for a quick clean if needed, but I wouldn't consider one as primary to use at the bench.
Plain cotton patches for me, along with Wipe-Out foaming cleaner takes care of 90%.
Plenty of quality cleaners out there, some (like Wipe-Out) remove both copper and carbon fouling, others are more specific.
That's for a whole 'nother thread.