First thing I would do is start drawing what I think I want the outside to look like and that includes all the switches, displays and hoses. The second thing is to then redraw that using scaled measurements so you’re sure things fit and look the way you’d expect in real life. Third is to start with another drawing from the top-down view and try to position the things you know will be inside starting with the larger stuff and things which might require positioning relative to the outside feature.
It might end up being a simple box with a bunch of stand-offs to hold the pumps and holes in the sides/top/etc of the box for hoses, switches, etc. It might not be so bad a design or it could be quite complicated.
Just to let you know, I once paid about $50,000 for a product design and prototype. Then I learned how to do all of that stuff over about 20 years. Good skills to learn even if just the basics.
Thank you for the answer!
Just to be clear: this question only asked about making the casing for the 14 pumps, not at all anything else (the screen, etc.).
Since I am at prototype stage, even a plastic (resin?) box would do, with the pumps screwed at the bottom and the tubes sticking up (and cables coming out of the side). Consider that putting 14 of those pumps in a box would make a box about 65cm long (!) and quite narrow. It would only need to be splash resistant, and cannot be made of wood.
What would you use to build such a box?
Part of prototyping is figuring this stuff out and I don’t recall seeing that the pumps must be mounted side-by-side it’s new info. Since this is a prototype, I don’t see why wood can’t be used. Those pumps shouldn’t leak nor the hoses and a bit of paint on the wood would be protective enough for a prototype. If really worried then you could place a sheet of plastic(overhead projector sheets?) on top of the wood.
I would reconsider the reason why you say the pumps must be side-by-side. Is it the pumps or the hoses(input/output) which need to be side-by-side.