Clean down with a light scouring pad to remove any gease.
Prime with this, it bonds to anything
https://www.screwfix.com/p/zinsser-b...ler-1ltr/29661
2 coats of good quality ( not from B+Q) eggshell, oil based or acrylic. I tend to use acrylic paint now as it's far better than it used to be
Apply primer and eggshell with these
https://www.amazon.co.uk/Density-Rol.../dp/B00J8PRUJC
Don't use the crappy white foam rollers, they won;t give a good enough finish
Most eggshells will be a tough enough finish or you could finish with a water based varnish
Take your time and as soon as it starts going tits up put everything away and start again tomorrow, you'll do fine