I think I would prime & paint first, then top-coat with poly.

Alternatively, you could use shellac as a sealer, paint, then poly.

 

You can tape off the maple banding with blue tape and paint the ply. However, be careful to press the tape down really well so the paint doesn't run under the tape. I don't think that will be much of an issue with a tight grain wood like maple.

 

Paint the ply before the glue up. Then you just have to keep it out of the spaces that get glue. Looks better, easier to paint too.

 

I think you will want the wood that is clear finished done first. If you don't get the tape sealed then the paint can be cleaned off the poly. If you get paint on the wood and it seeps under the tape, it will be difficult to remove. Just the way I would do it I think.

 

+1 for painting the ply before attaching the banding. then you can just poly the entire unit which will add durability to your finish

 

If you can't finish the painted and polyed parts separately I'd do the poly first. But make sure you give the poly plenty of time to cure. Especially if you're using an oil based primer or paint. You don't want a situation in which the mineral spirits in the paint can dissolve into the poly.

Lots of masking tape will probably make it doable.

 

I think painting before the edge-banding would be the ideal way. Assuming you're using solid edging and not iron-on (don't know if the heat would effect the paint at the edges). I think it'd be important to fit make sure your edging is sized and trimmed well before painting the ply. Planing/sanding of the trim could be done once it's applied to the painted ply, but it'd be more work to avoid damaging the paint than it would be if you just fit everything prior.