You can use enamels or acrylics, matte or gloss, by any number of manufacturers. I think you'll find that most of what we painters have posted here in the forum reflects a lot of personal preference, based on long-time experience, and that many of the paints are as good as the next.
Personally, I use both enamels and acrylics, whether matte or gloss, based more on the specific color, because I don't typically mix custom colors.
If I use a matte, and the final result is supposed to be gloss, I will use Future floor polish, which is a clear acrylic gloss, for the glossy surface. Conversely, if I happen to use a gloss, and the final result is supposed to be matte, I use Testor's DullCote matte to seal everything.
Generally, enamels will require powerful solvents, such as mineral spirits or turpentine; turpenoid, which is also a mineral spirit, despite the name; or even lacquer thinners. Oils use the same solvents. Acrylics can be thinned with water, or isopropyl.
Testor's enamels in the little sqare bottles can be found at hobby store chains like HobbyTown and HobbyLobby, but also Michael's and AC Moore. Hobby stores will probably also stock Model Master, which is another Testor's brand, and which includes enamels and acrylics. Tamiya also makes very good paints, both enamel and acrylic, as does Gunze-Sangyo.
Here is the States, if you want Humbrol, you will probably find it in a classic, mom-and-pop hobby shop, rather than in the contemporary stores.
Hobby shops that supply model railroaders will also stock several lines of good paints, again, in enamel and in acrylic, as well as other tools that scale modelers and toy soldier painters use.
You can also get good brushes at all of the places I've listed. I'll recommend that if you plan on painting on a regular basis, buy good natural fiber brushes, rather than synthetic. They may be more expensive to start, but they will last longer and work better, so you aren't replacing them as often. As the Frug used to say, "Frugal does not mean cheap, it means you don't waste anything."
That's some general info. For your specific task of painting K&C figures, I recommend looking at the links ecuriel posted, as well as browsing the K&C forum, because I've seen that specific topic--matching K&C colors--discussed at various times. Of course, someone may also add that info here in this thread, too.
Hope that helps, prosit!
Brad