MDF will fuzz up if you use water based primers on it. But, the best primer is shellac (alcohol) based, made by the company that makes "Killz primer". I used the shellac "sanding sealer" or the white primer - both work very well. Then very lightly sand and paint or clear coat. There really isn't a good reason to use oil based paint either. Acrylic paints work very well and are just as water resistant, plus they dry much quicker. Today's oil based paints in general are not very good. Our air quality regulations force the manufacturer to use less and less volatile solvent in the paint, plus alter the basic formulation. So, most pros use water based paint now, except for primer.
MDF does not swell in water like particle board does. If you left it in water for a long time it would swell, but getting wet doesn't bother it like particle board. In fact most siding and trim boards for houses are now made of MDF.
MDF is very strong in compression, but not in bending or tension. So, if you design the stand so no parts see a bending load MDF can carry the weight just fine. But, it is very, very heavy. The best idea, as Spar said, is to use two by something wood for the load bearing frame and just cover it with MDF for the finished surface.