For MDF I wouldn't use anything except a vacuum and tack cloth to clean the dust prior to priming. MDF is too absorbent. Cleaners, including plain water, can make the surface swell. Some solvents will actually dissolve the adhesives that hold MDF together, or at least make it swell. Wet MDF dries from the outside in...when the top layer cures it actually locks in the moisture underneath.
Use a quick-dry solvent- or lacquer-based primer. On the West coast of the US the Zinsser products are popular:
http://www.zinsser.com/subcat.asp?CategoryID=1B-I-N and Cover Stain are quick-drying and sandable. If buying it in gallons make sure to have it tinted first. Only tint it to half-formula of your top coat: gray primer for black paint, pink primer for red paint, etc. Two or three rattle-cans also work just fine if you spray even coats.
Make sure to wrap yourself in wet sheets and put undies on your head.