Using an air brush will give a superior finish than painting with a paint brush. However. You are painting MDF and here lies the problem. It is difficult to get a really good finish on MDF, especially on the edges. If I were in your shoes then this is the way I would go about it. I would spray the MDF with a spray on sanding sealer, it will probably need several light coats and a rub down between coats with something like 400 grit. When you can no longer feel any roughness than it will be ready for the acrylic spray on paint, again the several light coats are better than a couple of thick ones. Prior to spraying it for the last time leave it over night for the paint to fully harden before the final coat.
I see many things in shops, especially department stores that have items made from MDF, but most people don't know this, the finish is really good but then it has been applied in factory conditions with professioanl equipment but then again they are churning out thousands rather that the odd one now and again like the hobbyist would. It is a pain staking business getting a really good finish on MDF and I hope it goes well for you.
