My aunt painted her cabinets a couple years ago. They were varnished wood. All she did was scuff them quite a lot, then paint with an oil base paint- 3 thinner coats looks better than 2 thick ones.
OR- you could also paint with a water based primer first and then water based paint, if you want to avoid using oil paint.
I would cover the grain, personally, but that's just an individual preference thing.
Melamine is good, but
-it can yellow with time.
How about painting them the same colour as the trim, constrast makes a room look smaller and red and white is kinda jarring.