Are you planning to laminate after assembly or before? And are you planning full side art? Those are your two biggest questions because it can drastically change your options.
If you are planning to screw it all together and then fill holes and laminate, you have to consider how you are going to do the inside surfaces because some of it will be exposed. Then you also have to consider the "non-side" surfaces like around the bezel, under the marquee, around the CP, and below the CP. These can all be tricky if you don't want to paint.
But if you have plans that involve laminating beforehand for those pieces, then you might want to consider melamine.. it is already a laminated surface and it comes in 3/4". And with careful consideration in your build, you could save a HUGE amount of finish time.
The side art is a huge part too because if you do plan to use full side art, you can use melamine or go with ply or mdf with laminate on the inside side, drill and screw or glue and nail, then fill holes, sand smooth, seal the wood with a layer of spray primer, sand smooth, and apply art and never really have to deal with painting.. (with melamine you would just sand it smooth.) I don't consider spraying on a few cans of primer to be painting because it is so simple and you sand it afterwards so it doesn't matter if you are careful. I primed my CP with autobody primer from a spray can, waited a day for it to fully cure, sanded to 220, sprayed a second coat, waited a few hours, and then sanded to 320 and it was like a glass surface, perfect for applying vinyl. If I had done my sides in full vinyl I wouldn't have gone any further than that on my sides.
I thought about using melamine but then I would have had to use a method of construction that didn't involve screwing or nailing from the outside. Certainly possible but a little more tricky. I thought about laminate too but the added thickness was one issue as was trying to laminate the surfaces that are visible but impossible to use a router on to trim, or surfaces like my bezel where it is rounded. It would have been more work in the end than just painting. Once I had to prep to paint those surfaces, shooting the outer sides was a no brainer. Plus I figured worst case, I was going to eventually put art on the sides anyway.