The finish matters less than the prep with MDF, mate — but get both right and it'll look like solid joinery.
The problem is the cut edges. The faces of MDF are dense and seal up nicely, but the edges are like a sponge — they drink paint and dry fuzzy and rough. So before any topcoat, seal those edges. Zinsser BIN (the shellac one) or a coat of dedicated MDF primer knocks the fluff back. Sand to 240 grit between coats and you'll feel it go properly smooth.
For the topcoat, you want eggshell or satinwood — a mid-sheen trim finish, not wall emulsion. Two good reasons: it's harder and more wipeable (MDF often ends up as skirting, shelving or built-ins that get handled), and a bit of sheen reads as proper woodwork rather than a flat panel. Little Greene Intelligent Eggshell and Benjamin Moore Advance (a self-levelling waterborne alkyd) are both cracking on MDF — they flow out smooth and harden right off. Dulux Heritage Eggshell is the budget-friendlier option and still very tidy.
The "but what about full matt?" question: you *can* use a matt finish if you're after a contemporary flat look, but only over properly primed MDF, and accept it'll mark more easily. Earthborn Eggshell No.17 is a low-sheen, breathable option if you hate shine but want durability.
Colour-wise, MDF takes anything. A soft off-white like Farrow & Ball Pointing or Slipper Satin keeps trim quiet; for built-in shelving with a bit of drama, Card Room Green or Inchyra Blue in eggshell looks the business.
Practical bit: thin your first topcoat very slightly, lay it off lightly, and resist overloading the brush — MDF shows every drag mark. A 4-inch foam roller for the faces and a good synthetic brush for edges gives the cleanest result. Three thin coats beats two thick ones every time.