Depending on whether it's just decorative or to be used as (e.g.) a step, 6mm or 12mm ply should be fine. Screw a couple of pieces of scrap to the vertical wall to act as batons and you're laughing.
Depends whether you want to spend the time filling any gaps if they're butted together or whether you can get a nice clean line with them being mitred. Not much of a difference really.
I'd also use a thin baton to hold the two pieces together so that if you accidentally kick the vertical, it doesn't cave in underneath the horizontal.
Personally I usually build boxings for customers out of mdf then you haven't got the edge to sort out, that you do with plywood, but like you've said if you mitre it then you don't see that edge I always use 3 battens for boxings:
Jonzun's approach is really good - if you get a good fit then you can also leave the top sheet loose if you want in case you need access to the pipes in future. Can't go wrong with that as a structure though.
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