Manufacturers use different methods and materials for sizing watercolor papers. Internal sizing is mixed with the paper pulp and external or tub sizing is applied to the finished sheet of paper. Some papers have both. A heavily sized paper may resist paint a little too much, so sometimes I lightly sponge a sheet of paper before I begin to paint to soften the sizing. If you stretch your paper, you probably won't have this problem.
Hot press is very smooth, rough is highly textured, and cold press is somewhere between the two.
Cold press is probably the most commonly used because watercolors are harder to control on smooth paper and rough tends to create more texture than many artists prefer. Paper surfaces will differ greatly from one manufacturer to another, so you may find a cold press that seems more like hot press or a rough that is extremely heavlily textured. The side you like best. However, most paper surfaces are different front and back, so choose whichever you prefer. Ask your question on Supplies.