The finish matters, but on melamine the primer matters more. Melamine is a glossy, non-porous plastic laminate — paint simply won't grip it without help. Skip the prep and your lovely topcoat will chip and peel within weeks.
Here's the order of play. Degrease thoroughly (sugar soap, then a methylated spirit wipe), give it a light key with 240-grit, then prime with Zinsser BIN — a shellac-based primer that bites into shiny surfaces like nothing else. For larger jobs Zinsser Cover Stain works too, but BIN is my go-to for slick laminate. This adhesion layer is non-negotiable.
For the topcoat, go satin or eggshell — never matt. Melamine surfaces are almost always doing a hard-working job: kitchen units, wardrobes, shelving. They get wiped, knocked and grabbed. A satin sheen wipes clean and shrugs off knocks; matt just holds grime and burnishes where you touch it.
My honest recommendation: use a purpose-made cabinet paint rather than a wall eggshell. Bedec MSP (Multi-Surface Paint) in satin is brilliant on melamine — tough, self-levelling, and it cures to a properly durable finish. If you want a designer colour, Little Greene Intelligent Eggshell or Dulux Heritage Eggshell both lay down beautifully over BIN primer and give you a wider palette.
Colour-wise, soft greys and muted greens hide kitchen life better than brilliant white. Farrow & Ball Cornforth White or Pavilion Gray are classic for units, while Little Greene French Grey - Pale keeps things light and warm. For a quieter, deeper look, Dulux Heritage Eggshell in a smoky neutral works a treat.
The "but what about a roller mark" question: use a short-pile microfibre roller for the flats and a good synthetic brush for edges. Thin coats, two of them, and leave a full day between. Don't rush the cure — melamine paint can feel dry in hours but needs a couple of weeks to fully harden, so go easy on the wiping early on.
Get the BIN down first, finish in satin, and it'll last for years.