Paint Kit
Starting off with watercolors may look expensive, but you can assemble a high-quality sketching kit for not too much. One route is to purchase a half-pan set. The Windsor & Newton Cotman Sketcher's Pocket Set is a good starter kit, and is small enough to travel with. It has 12 colors in half pans, a tiny (though very nice) brush, and mixing areas in the lid. The next step up is the Cotman Field Box, which has same number of colors but it is a larger box, has a water container, and more mixing area.
The small box is perfectly adequate. You can use a tiny water container like a film canister (which won't leak) if you are carrying the kit with you, or use a cup or an empty jar if you are working at home. I have a collection of old peanut butter jars that I've been using for paint water for years. I found a teeny-tiny Naglene bottle with a screw-on lid that I've had in my bag for water. It is about the same size as a film canister.
If want to make your own sketching kit, you can buy paints by the tube and just purchase the colors you know you will use. Watercolor paint tubes go on sale pretty often. If you are patient, you can get a full set for a reasonable price. Squeeze out the paint into the paint wells in a small closing box and allow them to dry. Just get the paint wet with a few drops of water to re-activate it. I like the Windsor & Newton Cotman and Grumbacher Academy paints. These are both "student-grade," but they work great for me. In the Illustrated Watercolor Journaling class I took a couple of years ago, we made a full color wheel using only these six colors: Cadmium Red, Alzarian Crimson, Ultramarine, Cerelean Blue, Lemon Yellow, and Cadmium Yellow. Mix Cadmium Red and Cadmium Yellow for orange, Alzarian Crimson & Ultramarine for purple, Lemon Yellow and Cerelean for green. My personal kit (since I already had tube paints, I just bought a travel palette and added paint) also contains Sap Green, black, Yellow Ochre, Indigo Blue and Payne's Grey (for the best shadows ever). You can do just fine with just the six colors, and that Cotman kit obviously contains more. Ignore the white paint. You don't need it.
For an even smaller paint box, purchase empty half-pans (Daniel Smith sells them, if you can't find them locally) and fill them with tube paint as described above. An Altoids tin will hold 12 half pans, but other small tins of comparible size would also work. Attach the filled pans to the inside of the tin with double-stick tape, adhesive magnet strips, or adhesive velcro. You can use the opened tin lid for mixing colors.
Brushes
There are lots and lots of watercolor brushes available. The selection can be positively overwheming. Synthetic, sable, mop, lining... what does it all mean? I'll save that for another article. For basic sketching purposes, you'll want something that will perform well, fit in your sketching kit, and is cheap enough that you won't be devastated if you accidently leave it on location. My favorite sketching brush is a #8 round, but you could get one a little smaller. I wouldn't go smaller than a #4, unless you want to paint in very great detail! Sable brushes are the most expensive, but you can also get sable blends and synthetic brushes of very high quality.
What you don't want is a brush that will drop its hairs while you are painting, or that doesn't hold its shape. Look for a nice pointed shape to the brush tip. Run your fingers back and forth over it and then check to see if it has returned to a tidy point.
Your brushes will last a long time if you care for them. Don't leave them sitting, point down, in water. Clean the brush in fresh wather, then dry it on a paper towel and reshape the tip before putting it away.
Journals
For sketching with watercolor, you need a journal with pages heavy enough to take wet media. I like to paint on 140# cold or hot press watercolor paper, but others are happy with heavy card stock or lighter-weight watercolor paper. It is sometimes hard to find watercolor sketchbooks in stores. I've seen some spiral-bound versions. Think about what you like in a book - spiral bound or hard bound? Portrait or landscape orientation? What weight of paper? Most of the books available for sale in local art stores don't appeal to me, so I make my own sketchbooks. Contact me if you are interested in a custom watercolor sketchbook. You can make your own simple sketchbook by cutting sheets of watercolor down to your preferred size, punching holes along one edge, and binding them together using medium-sized binder rings that you can purchase at any office supply store.