Selection of tube watercolor paints- any reputable brand such as Da Vinci, Winsor-Newton, M. Graham, Holbein, etc. At least one red, yellow, and blue plus an orange, green and purple. My current palette includes Permanent Rose, Cadmium Orange, Arlide Yellow or Aureolin Yellow, Cobalt Blue, Manganese Blue, Hookers Green Dark, and Mauve. All are Da Vinci tube watercolors. I often use Paynes Gray and/or Burnt Umber for small value studies.
Brushes: Round brushes in approximate sizes 8 or 10 -can be synthetic, squirrel, or sable (red or Kolinsky)- plus a one inch flat synthetic brush. I also use a 1 ½ -inch flat brush with camel or synthetic-natural hair blend. Dick Blick has a good and affordable brush assortment, including their Master Series of Kolinsky sables (I find the no. 10 very useful). AC Moore also now carries some Winsor&Newton rounds, pointed rounds, and riggers at affordable prices (use the 40 or 50%-off coupon). Finer brushes such as no. 2 or 3 riggers and small lettering brushes (I like the no. 4 Webb liner from Cheap Joes Art Stuff) can also be added.
Paper: I use Arches 140 lb cold pressed paper exclusively (natural, not bright-white) and you can choose it or another high quality watercolor paper. Again, AC Moore carries these and with a 50% coupon are roughly $5 for a 22 x 30 inch sheet. Or you can choose to start on cheaper paper available in pads at most art supply stores.
Palette: You can use something as simple as a dinner plate, or butchers tray, or one of the many watercolor palettes sold at art supply stores. Be sure it has a fairly large mixing area.
Other useful supplies include a spray bottle, sponge for dabbing water off your brushes, water container, drawing board (gatorboard from Cheap Joes, plywood, masonite, etc), masking tape, bulldog clips, and razor blade or other device such as palette knife for scraping.