You have a couple of choices here. I use a little Winsor Newton Cotman
watercolor set which combines twelve small pans of color with a tiny water
bottle, a water cup, and small---virtually useless---brush. Basically it
is an ingenious gadget, and I have always been a sucker for gadgets. The
whole affair is not much larger than a pack of cigarettes. When the cap is
taken off it becomes the water cup, and unfolded it reveals the pans of
student quality watercolor, three mixing surfaces, and a tiny sponge. For
paints, palette, and water cup, this is all you really need. There are
other tiny kits with pan colors on the market, so look around and choose
the one which pleases you. Many of these firms also manufacture pan colors
in their professional grade pigment, and you might wish to upgrade to the
more costly paint.
The other alternative is tube colors. I use tube colors for all of my
studio painting, but for me the pans are more convenient for quick
sketches outdoors in a small scale. If your little pans run dry (for me
the blues usually go first), you can squeeze some tube colors into the
pan, and that will see you through. If you choose to pick your own tube
colors, you must then find a portable palette for mixing the paint. This
is a bit messier and bulkier, but certainly a viable option.
Many teachers suggest two of each "primary" colors, plus some "earth"
colors. This might include cobalt and ultramarine blue, cadmium red and
alizarin crimson, Winsor yellow (other manufacturers use their own brand
names), cadmium yellow, and the "earth" colors burnt umber, raw sienna,
and burnt sienna. All of these colors plus some greens are in the usual
set, such as the Cotman box described above. If you really want to
simplify, choose one blue, one red, one yellow, and perhaps the burnt
umber or burnt sienna. You will be amazed at the range of color you will
get by carefully mixing three or four colors! And your result will
probably be more harmonious than if you used the thirty color box---which
you would be wise to avoid in the first place.