My personal opinion is that mesh is better. Yes, a little bit of spray may come through from below, but water cannot stay on the tramp because it drains off immediately through the mesh, and air circulates through, drying the tramp quickly. A solid tramp can collect little puddles of water where people are sitting; and once it gets wet, it stays wet much longer because no air is circulating through it.
For the same reason -- air circulating through the tramp -- a mesh tramp also is cooler for the passengers than a solid tramp.
Also, of course, a mesh tramp makes a boat a little bit less susceptible to capsize because air can get through it and the wind cannot get quite as good a grip.
You also asked about color. Can't help you there. I figure that theoretically black would be best if you sail in cold areas because it will absorb the heat of the sun and that white would be a better color if you are sailing in a hot area because it will reflect the sun's heat away and the tramp will be cooler. But black is easier on the eyes and easier on the skin because you don't have as much sun reflection off the tramp. So I would say, overall, if you had to choose between black and white, black would be the way to go. But if you want something prettier, Hobie has a really nice greenish tramp -- I don't know what color they call it. Maybe it is teal. I'm not very good with weird color names. Anyway, that color of mesh tramp is on all our Hobie Waves, and those tramps have held up extremely well for a number of years in the ruthless South Florida sun.