The sad truth in life is that one is much able to properly critique instruction (of any subject) AFTER one has mastered the subject than when [first] learning. I don't know your level of ability, but you seem to have some interest in the matter and I presume some actual experience in 'shooting' at least.
Basic Marksmanship should cover stance or posture, grip fundamentals (possibly both single handed target work and two handed defense shooting configurations), breath control, sights, sight alignment, sight picture and trigger release (or squeeze, pull, stroke or in my case 'convulsive spasm'). This class will include how to fire a well aimed single shot, and possibly how to put several well aimed single shots together for 'timed' or 'rapid' fire.
Self-Defense should cover legal aspects of defensive shooting. What - IN YOUR STATE - is 'justified self-defense'. (Most places are fairly similar, but the small details can cost a great deal of attorney fees and incarceration time if not correctly observed.) The shooting portion should include concepts like mental preparation, types of practice for self-development, actual 'targets' on the human body - and possibly on predatory animal bodies if such problem presents. The difference between 'target' and 'combat' sights, 'flash' sight picture, 'lead' on a moving target, concepts of 'cover' and 'concealment' and deescalating techniques.
In general terms, I would suggest an instructor with law enforcement background over an instructor with solely military background for self-defense training. The rules of engagement and mindset for defense is different between 'citizen-defender/lawman' and 'soldier'. There are some glowing exceptions, of course. The downside is many lawmen types have a built-in persona of 'in charge' and can be a bit difficult with whom to deal. Again, some glowing exceptions.
Also, bear in mind that firearms trainers are often their own biggest fan. Most have worked very hard to become proficient with small arms, and jealously protect their accomplishments. Some of them are as good as they think they are. Some aren't. But as in much of life, one cannot always tell ahead of time.
Also, some instructors may be very well versed in the mechanics of gun handling, but very poor in legal knowledge. If nothing else, a self-defense instructor should know the appropriate sections of law for your state and at least show you where to look up the law so you aren't totally ignorant.