For your use you can put the varnish straight onto the MDF, Dilute the first coat with 10-20% white spirit. Rub down between coats with something in the region of 240grit abrasive particularly afyer the first coat which will raise the "grain" more so on any cut edges.
You may find a waterbased finish easier, something like Dulux diamondglaze, this will seal it sufficently and if you do as I said elsewhere use exterior or at a minimum moisture resistant MDF that will help.
Jason