The best cleaning kit is the one you assemble, all those premade kits from Outers, Hoppes, Breakthrough, etc...are pretty much big box store shit.
There's going to be various opinions regarding brands but the recipe for a good cleaning kit is:
1. Cleaning Rod: One-piece, coated or carbon fiber, free rotating handle, longer than you think you need. Tipton, Dewey, Pro-Shot are all good companies that make a product that will serve you well. For cleaning the chamber, get a pistol cleaning rod, the handle won't rotate so you can spin it in the chamber.
2. Brass Jags: I mostly use Parker Hale type...forget spear-type or patch holders. They look like this:
If you get them from Dewey, you made need an adapter if you intend to use them with other cleaning rods since they are female threaded.
3. Brushes: I use them sparingly but nylon brushes work ok but not as well as bronze phosphor, however BP bore brushes can give you a false positive regarding copper. Regardless, I mostly use these to clean the chamber anyway. Dewey and Proshot make really good brushes.
4. Patches: Cotton flannel patches from KleenBore are great.
5. Bore Guide: Get a bore guide specifically for your action, the universal ones suck. I've used the Possum Hollow ones for years and they work well. Get the solvent port if you get one.
6. Toothbrushes: Get GI-Type toothbrushes, Otis Tech makes some damn good toothbrushes, with blue bristles.
Get ones that look like this:
Not these, these suck:
7. Solvent: There's a wide wide world of solvent out there, there's bore solvent, copper cleaner, foaming bore cleaner, etc... I've generally gotten by with Shooter's Choice MC-7 and if I need to do a quick clean I'll use a foaming bore cleaner.
8. Rags: white or blue shop towels, old t-shirts work ok too
9. Q-Tips: Don't get ones with a plastic stem, get one with a cardboard stem that you can bend to get into nooks and crannies.
10. Picks: Steel dental picks, the plastic ones are crap. They're good for getting goop out of nooks and crannies but also getting o-rings out, gas rings, and other stuff.
11. Flashlight: Doesn't need to be high lumen but a bendy neck is good and a magnetic base is handy too.
That's about it for the basics, from there you can specialty tools if you want like chamber cleaners and stuff. Lens cleaning wise a pack of Zeiss wipes and some Spudz microfiber clothes are going to take care of 95% of your glass cleaning needs.
These deep Plano Stowaway containers do a good job of holding most of that shit too.