Cleaning kits and particularly lubricants are a matter of religious fervor to a lot of folks. Be prepared for a lot of opinions and advice here.

If you only have one thing, Breakfree CLP is the thing to have. It isn't the very best cleaner, lubricant or protectant, but it does all three competently. I keep a bottle in my BOB.

At home I use Hoppes as a bore cleaner, although Shooters Choice is just as good. For most of my guns I use a Tuf-Cloth with a few drops of liquid Tuf-Glide on bearing surfaces. This has worked well for me in competition and some very intense training.

Other than a rod, some patches, and a cleaning brush (gun cleaning brushes outperform toothbrushes in my experience) I'd also get a Boresnake, some disposable shop towels, and something to help you get into small places. I like CountyComm's Universal Cleaning Stick, but you could easily improvise something that worked well for you.

Follow each gun's manual carefully on disassembly, reassembly, cleaning and lubrication.

Whatever else you do, keep all ammo out of the cleaning area and check to ensure the gun is completely unloaded. Check twice. Check every time you even look away from the gun.