As with others a pre made mdf primer is best. Sure you can mix pva and water and paint that on, but its one of those q1uick fixes and never seems to sand as well as it might. In that I dont think it penetrates enough and by the time its smooth, you’re through in places. The pre made will have penetration and drying added.
MDF primer is suitable for the entire board, all faces, the main flat faces are already smooth, its just any machined parts or the edges that might need a couple of coats, sanding to 240 grit inbetween, yes damn those edges.
If you dont sand and seal, and sand again the edges or machined bits take on a fluffy appearance when a finish is applied, oil, paint etc.
MDF is under appreciated as a medium for making furniture or internal joinery. Many start off bias, considering it a less worthy material, but in use and with ingenuity, its great stuff, but the dust isnt, and tends to be able to render itself down to sub micron size no matter how you cut it so a dust mask is a given.