What's a good cleaning kit and a lube that you recommend for a handgun?
I'm not much for kits, actually. I will buy a kit if I'm in a "starting out" situation (such as moving to Hawaii but not shipping my cleaning supplies), but my kit does not stay stock for any length of time.
First, buy a sorting container. I use a fishing tackle box, but am in danger of outgrowing it.
Second, buy the "universal" parts. I like segmented ramrods because they are variable length and easy to store. Buy 2. If the rods don't come with bore guides, buy 2 of those as well.
Third, buy your choice of products. I use Break Free CLP mostly these days (available at Security Equipment), because it acts as both cleaner and lubricant. I also use Hoppes #9, partly for sentimental reasons, for any soaking jobs.
Next, buy caliber-specific parts. For every caliber, you need a bronze brush, a brass jag, and maybe a stainless steel brush. And, for .22 caliber only (including .223), buy some Hoppes-brand cleaning patches. Anything else will be too thick for easy use in the bore.
Now, assemble some recycled parts. Old toothbrushes come in handy. Q-tips. Tongue depressors / Popsicle sticks. And old white t-shirts. Old white T-shirts can become gun rags or cut into 1 1/4" squares for large-bore cleaning patches.
Voila! Your all-purpose cleaning kit!
A note on shotguns... do buy a specific shotgun cleaning rod. They are far thicker than other rods. Also, don't buy a jag for shotguns... if your barrel has any choke, getting a jag and patch thru it can be quite difficult. Just wrap a cotton ball over the end of the rod and wrap a 1 1/2" patch over that.
I also bought a 2' x 4' folding epoxy table from Costco or City Mill, I forget which. It lives folded behind the bedroom door, and only comes out when guns get cleaned. Not only do I always have a table space to clean on, it is resistant to the various solvents and such involved.