As a starting point, and given the the overall idea, I would advise you to :
- put a 5mm thickness on your "lateral supports"
- put 10mm on the base thickness
- put 1,5mm of shell thickness
- put 25% infill.
- add 5mm chamfers in all corners
That is industrially strong !
Made a 5mm pla bar the other day. 4 shells 20% infill. Could just about flex it a mil or so, no chance of breaking it.

For strong stuff I use 2mm - for really strong stuff I use 4-5 mm.

Got a large plant trough with extendible legs - that's 4mm walls, It'd take a sledge hammer to damage the things.

To give you some kind of idea how strong 2mm pla is (and most other plastics are at least as strong).

The white thing on the drill in this video has walls made from 2mm pla, and yeah it's also pretty flexible, don't believe half of what these guys tell you about pla ;-) :



5mm I could jump up and down on.
I did stand on the plucker to test it's strength. About 90 kilos on the hoof.

Surface pro's don't weigh much.

And I don't get how a flat piece of plastic is a holder.

The answer to your dilemma has already been mentioned.

Find someone local to you on: www.3dhubs.com. They should be able to help you with the design and also print way way cheaper than someone like shapeways.