Tony,
First off, you only need to work in 2D. The 3D component is only if you want to progress to 3D Printing. Also, I don't think you'd be competing with anyone really. It's just a different material really.
I've been cutting styrene overlays for coach sides and scratchbuilding for years and the lowest thickness which can be used is 0.25mm, though you could probably go up to 0.4mm in some circumstances. The issue is that laser cutters tend to burn styrene unless you have a machine that can be throttled down on power and speed. I use a Thyme Graphics Silver Bullet Pro which is a bladed cutter, rather than laser. Just a smattering of projects on the workbench -
Apologies for potato quality
There's a very interesting thread on same here on RMWeb - http://www.rmweb.co.uk/community/index.php?/topic/108310-darkly-labs-emblaser-affordable-laser-cutter-review/page-30, particularly where it talks about health risks with the fumes, minimum thickness being 1.5mm and so on.
I'd experiment like mad if you have the facilities, and try a host of materials - perspex, styrene, whatever you can source, and let the results dictate what's possible. I'm keen to get a laser cutter at some stage of 2017, and would be delighted to hear your musings/results.
Richie.