Paper is where to spend the money - buy good watercolor paper. The cheaper paper is like working in sludge. You can get away with using student grade paint (such as Cotman or Academy), but not student grade paper. I get cold press either 140 lb (and stretch it) or 300 lb. My favorite paper is Winsor & Newton 140 lb. cold press paper. I also use Kilimanjaro cold press 300 lb. a lot. It works OK (it is economical and I do a LOT of paintings and use a LOT of paper). I prefer Arches 300 lb. cold press, but it's rather expensive.
I stretch my paper on either thick foam core or hemasote (my favorite and purchased at a lumber yard). I do this by wetting both sides of the paper and stapling it to the board while wet.
I have my students get Daniel Smith or Windsor and Newton or M Graham (or other artist brand paints) in tubes (student grades can be used if money is an issue). They start with Quinacridone or permanent rose, Aureolin or lemon yellow, and indigo. A whole lot can be done with those 3 colors. Later on I have them get pigments such as Permanent alizarin, Burnt sienna, cobalt or ultramarine blue, New gamboge, viridian. They either get a small palette or use a plate or tray or paper plate.
I use Lowe Cornell Ultra Round watercolor brushes sizes 2, 6, 10.
I have a water container and an old hand towel or wash cloth (to manage the water on my brush, this cuts way down on paper towel usage), paper towels, a small spray bottle (get at walmart or a drug store in the cosmetics department).
I also use things such as masking fluid (rarley) rubber cement (also a resist), salt, plastic wrap,etc. These make textures or marks. You do not need them to paint.
Hope all that helps. Everyone has slightly different things they use so try things and find what you like.