Some of the guys here have had success with using a fine foam roller. Some like to spray. For Dracula, I used a latex based paint, custom matched at Lowes, for the base. I sprayed the yellow and black, also latex, but didn't like how they looked. I sanded it back down with 120 grit, shot 3 more thin coats of the base and am re-stenciling, using spray can oil based. It takes a lot of experimentation, but isn't really that hard.
I HIGHLY recommend you take a scrap piece of plywood, prime it, and replicate each step of the project on the scrap before spraying the actual cabinet - base coat..see how it dries and turns out, how many coats you need. Put some stencil material on the scrap, cut out some odd shapes, spray very thin coats. See how that goes, etc.. You can avoid making mistakes on the real project, see if one type of paint possibly reacts with the next, see what happens if you spray a stencil layer too thick, see how many thin coats to 'just' cover, etc..
One of my biggest mistakes early on was getting the paint too thick - too many coats. The goal here isn't a protective finish, like a metal railing, it's just to color..to replicate the artwork. The factory finish and stencil layers were as thin as they could do and it look good. More paint = more cost, in the factory setting. Good luck.