Paint & sand & paint & sand &..
I used primer paint, coated the parts, then sanded the first couple times with 120 grit. 3 or 4 coats to fill the "grain" and get a somewhat smooth surface. The last couple coats were sanded at 220 grit because things were getting smoother. Then, at last, I'd spray on the top coat.
You never really do get all the grain out, but that's ok. If you did, you'd be getting into the "fill" layers and that would be a nightmare!
Also I used a foam sanding block. This is important. Use a block to level stuff out.
As for paint I used name brand, rattle can spray paint.
Actually there is a writeup..