Buy a miniature watercolor kit. These are available at most art stores and come in a variety of styles. The basic type used in schools, with a rainbow of ovals of paint, is fine, although there are often smaller kits available with better quality paints. The type of paint doesn't matter, so your selection should be based on the size and style of box you like and your price range.
Find the right kind of gouache. There are two major types of gouache: traditional and acrylic. The acrylic has several advantages, including a wider range of colors and lower price. However, for this project, it's important to get the traditional type, because it can be dried and rehydrated, while the acrylic cannot.
Choose your basic colors. If you want a good range of color possibilities, start with a minimum of red, blue, yellow and black. Using these primary colors, you can mix most other colors. However, if there's a particular mixed shade that you really like, it's a good idea to get it, because mixing precise color matches can be tough. Other good colors to consider include white (which is opaque, so it can be used almost like correction fluid, or for painting on colored surfaces), magenta (which can produce a unique range of pinks and purples that you can't get from regular red), silver and gold.
Take the paints out of your gouache kit. If they don't come out easily, carefully flex the case a bit to help pop them out. If this doesn't work, as a last resort, you can soak and wash the paint out, although, of course, this ruins the watercolors.
Squeeze a bit of gouache into each empty pan of the kit. If you will be mixing colors, you can mix them now, or just dry the primary colors and mix a bit of each when you are ready to paint. Leave the kit open while the gouache dries, which could take several hours or more depending on the size of the kit.
Add a small paintbrush and a bit of rag or sponge to your kit. Travel brushes that hold water in the handle can be especially convenient for this purpose, but if you don't have one of these, put a few drops of water in the lid of the case when you're ready to paint and use that to keep your brush wet. The rag or sponge should be used for wiping your brush between colors, and can be washed or replaced when it starts to get covered with paint.