I work for a company that makes scientific equipment. We apply a few basic criteria, which narrow things down a lot.
First, a lot of those fasteners are either really specialized or just rare or obsolete. So they can be ruled out.
We look for something that will be easy for our assemblers, and for our field service technicians. They have given us feedback on what they like and dislike, including what kinds of tools are common in different parts of the world. They hate flat head screws. Hex socket screws are really easy, and it's also easy to make them look nice on an assembly.
To an increasing extent, we want tools that can be used with a torque handle. For instance hex drive is better than Philips in that regard.
I hate to say that it's still a work in progress, but we are heroically trying to get away from fractional drivers, especially for our field technicians who presently have to carry full sets of US and metric tools. We even have mixtures of US and metric in some products!
If something is meant to be serviced by a customer (e.g., a lamp or filter that gets replaced), then we stick with Philips, which we are told is common worldwide. Or we use a captive knurled fastener if it's in a place where there's finger access.
So these are just a few thoughts. Other considerations are whether you're in an industry that has already standardized on a particular tool set, such as metric allen wrenches for bikes.