So you do a coat of clear varnish last to protect the paint? I'm painting with a white paint (white dove). I'm guessing this will be necessary to keep it clean?I think you have already primed? I'm assuming water-based? Don't skimp on the quality of your paint. I use SW ProClassic; there are other similar ones. It's easy to have it color-matched to your van color if you so choose. For example, the white of my ceiling is the same as the white of my van. I regularly use Satin.
If you have any bare wood left, I highly recommend General Finishes Enduro-Var Satin. It is expensive (~$30/qt) but worth every penny and you don't need much. I cannot adequately express how good this stuff is, both for applying and wearing. Water-based but amber like oil. Dries to the touch in about 10 minutes. Bubbles are never an issue. If I had known sooner, my van would have more natural wood--Enduro-Var cannot be applied over stain or even shellac. After the first coat, lightly run a single-edge razor blade held vertically across the surface. This gently removes the nibs. For some surfaces, this could even replace sanding.
I would not use any oil-based finish in the van simply because it will stink for so long in that enclosed space and would not be good for the lungs.
I would not use cheap brushes. For no more money, you can use foam brushes which give a better result and can be easily rinsed and reused. Actually, I've contemplated a post about the hero of my build--one foam brush that has applied every drop of white and green paint used in my build and is ready for more. The foam brush also makes edges easier.
Sanding is critical before and during. After sanding (or the razor blade), wipe with a slightly damp paper towel.
Speaking of edges, stroke from the inside to the edge and lift as you approach the edge (think airplane lift-off). Never start a stroke at the edge. Don't heavily load your brush. You want thin coats, not blobs. Check your edges before you walk away, just in case. Also be careful of holes, like for your handles.
I tried a new-to-me technique in my van and am very pleased with the result. Because the luan had such a crappy surface, I knew that the normal feathering technique for a smooth finish just wasn't going to work, so I painted like a 4-year-old with short strokes totally random. Two layers of paint plus several layers of clear varnish, every stroke different. The result is a surface that prompts people to ask what material it is because the brush strokes make a subtle pattern.
Honestly I don't know what primer I got. I just got whatever the guys at the paint store gave me. I do a lot of business with these guys because I manage rental property so I do quite a bit of painting (walls not cabinets). They know what they're doing so I trust what they gave me.Varnish over paint is an individual choice debated endlessly by those who paint. In your case, I wouldn't because the oil-based varnish will yellow the white even more than it will yellow by itself because it is oil-based.
What primer did you use? If it is compatible with acrylic, you'd be better served by switching.