I did wonder if you where still here... I'm up to the neck in my own projects (as always) so I'm not really in a position to much other than share some ideas here. My advice would be to put as much of your thought process as you can here so as to let as many people as possible chip in - there are a lot of very knowledgable people here, including design engineers with experience in developing commercial products.
So... if you're talking about a device like the one I linked to that just shines a single laser beam, then I'd recommend that you try to get hold of a cheap one (perhaps even a broken one) to play with. This will give you an idea of the geometry of how they are set up as well as a feel for the kind of precision, rigidity etc that will be needed in the machanical assembly, and the kinds of speeds and moving masses you'll be working with. As I say, this should let you get a "feel" for the problem and help you visualise what you'll need to build - at least in the machanical domain.
As I suggested above, if you start with a ready-made mechanical assembly, you can move straight on to the electronic and software design. The Aduino seems to be most people's go-to choice for prototyping microprocessor systems and I believe that you can get motor controllers which will just plug in to them - minimal wiring required.
I should say though that Arduinos aren't my bag so I can't talk with any authority - I'm sure someone will have a recommendation for the specific boards you should buy?
The reason why I'm trying to pin down exactly what you mean by a "laser projector" is that the phrase laser projector can also refer to something else; that is, a video projector which uses a UV laser as its light source, in stead of a conventional lamp. These projectors are raster devices and use a colour wheel and an LCD (or it it a DLP... not sure?) and are a completely different thing to what I'm visualising.
So before anyone can make any useful comments, we need be certain of which sort of machine you have in mind!