Welcome to wet canvas…… First off you should build a cradle for the back to support the plywood and help keep it from wrapping. If you’re handy that cradle could give you a nice finished edge as viewed from the side so you may be able to get away from buying a frame if that is the look you’re after.

For how to prepare the plywood for paint, there is a current thread called sizing “hardboard” that will tell you all you need to know.

I made one mistake with plywood that hit hard during a painting. Sinking. Don’t forget to seal the plywood with some kind of primer sealer or I believe the plywood will suck the oil out of the painting, in blotches.

I’ve never had this issue with Masonite hardboard. A few layers of gesso on Masonite seems to be fine.

Yes, I should have said I prime my Masonite panels with acrylic gesso, not traditional gesso.

I have only had the sinking problem once in my life, and that was when I tried using a piece of plywood that was only primed with acrylic gesso.