Putting latex or any other water based finish on MDF is asking for problems. MDF loves to soak up water and when it does, it swells up like a sponge and the surface becomes very rough. Putting a varnish (poly or any other kind) on top of the latex will only accentuate bow bad the finish really is. I agree with the OP that an oil based paint would work best. There are many oil based paints from which to choose. Polyurethane paint such as Imron would be at the top of the list, but certainly not necessary to go with something that expensive.
If you want to cover it with some type of veneer such as Pergo flooring. Why not go with a particle board substrate whicn would cost less than MDF? Think about the weight of MDF. P,ywood is much lighter.