I started my diving career by entering the Navy as a diver (diving officer) and later became a commercial saturation diver, instructor, diving supervisor, diving superintendent and now am a diving project consultant for big oil (retiring this year).
Your questions don't lend themselves to a quick answer. The military is an excellent starting point, especially if you are involved in underwater construction (Seabees), or EOD. Construction is what it's all about in the civilian sector. Special operations is a waste of time if you want to be a commercial diver. Another alternative is if you are involved in land-based welding and NDD.
Landing a good commercial diver job depends upon your tickets, experience, and your school (affiliation). Other things like being ex-Navy put you into the same ring as other ex-Navy divers who may be in the position to hire you. It can really get complicated at times.
As you have seen already, people who have a construction/welding background are the first ones picked. This is for a good reason, as although diving is involved, to put it in context, it really is just how we get to and from the construction site. You have to be able to work when you get there.
As you are likely aware, there has been a lull in the commercial diving sector over the past decade or so. Some of the major diving projects that are slated to commence are in other countries like India and China, for example. You will likely to require an IMCA or DCBC ticket (unrestricted air), although you may get by with an ACDE ticket.
Like most jobs, experience is key. Don't be hesitant to work on-shore for a few years to gain experience. This is often the fastest way up the ladder. When you can, move to an offshore job. If you get a mixed-gas ticket and do well, you can consider a SAT job after you have the training.
If you want to discuss matters further, send me a PM. Good luck!