MDF is wood pulp fibers mixed with some sort of glue, or resin. If you make model buildings out of it, you really do need to seal it with Wood Sealer, or it will require many coats of paint, as it sucks it down into the fibers.
Once the Wood Sealer dries, the MDF paints up nicely, without being blotchy, or mottled. I use water-based Wood Sealer, without issue, on larger MDF pieces. Works superbly.
I've been using nothing but laser cut MDF bases (25mm x 25mm, 25mm x 50mm, 25mm x 75mm, and 200+ x 50mm squares), for several years now. I would recommend wiping them with a dry, microfiber towel, to gently remove the ash from them. Wear neoprene gloves, to keep the ash off your skin.
I paint my bases with PVA Glue, then I swirl them in a mixture of colored sands, after I have attached the mini's to them. I sometimes need to apply two coats for sufficient coverage, but I gave up painting MDF, long ago. PVA Wood Glue is the best PVA Glue to use, as it is stronger than White Glue. The typical yellow color of the Wood Glue can be an issue if you apply light colored sand to it (does not work for snow bases -- the 'snow' turns yellow -- White Glue only, for snow bases). Cheers!