Jack1,
I am no big expert but have painted a couple of kitchens (and am in the UK)
First of all, having taken off all handles and removed the doors I use Krud Kutter to degrease and sand down with whatever is needed to give a good key - 180 or finer
I use Zinsser Coverstain (oil based) or Zinsser 123 plus if you want a water based primer.
Using either Owatrol oil for the coverstain or Floetrol or XIM latex extender will help you get a decent finish.
Sand again with something very fine like 240.
I have never sprayed but roll using an Axus lime mini roller, then tip off with a good brush - Corona being my favourite.
As for paint, I like Mythic or little green, again, mixed with a conditioner like the ones mentioned above, and applied in the same way.
Brush marks are fairly easy to avoid this way, and it might be easier than spraying.
As mentioned, take a look at the traditional painter site -
http://traditionalpainter.com/
A lot to read, but a very good source of information !