You will want to build experience before buying your own truck, It's possible to do without experience first but having the experience going into it is big, Small companies are not always bad but definitely find a company that does shit right and remember when working for a company if they are into shady shit your reputation is tied to that and going into business with a bad reputation is not what you want to be doing so find a good company, and the advantage of bigger companies with heavies is you can learn about towing everything from light to heavy duty in time. starting your own company you will be dealing with light duty for quite a while but it's never bad to have the knowledge for it all. Wreckmaster is good, if you haven't already I recommend taking their in person hands on classes the knowledge you will gain is huge.
Now other than just finding a tow company to work for whenever you do decide to buy your own trucks you must know the barrier to entry is pretty huge for the towing industry so while you gain that experience at another company i'd be saving every dime you can afford to safe as you will need it, Truck payments, Fuel, Insurance, Damage claims, Equipment, Tires, Oil, etc there is a high cost barrier there, As for AAA the reason people say to avoid AAA is because it's not a good paying motor club, AAA offers volume over good rates, What would normally be 100 dollar tow might be a 50 dollar tow for AAA sometimes even worse, you can use them as a stepping stone but getting in a position where you depend on them is not what you want to do if you can when you start out with your company you want to get on police rotation, and again hands on experience is very important for police rotation you will get some very tricky calls as such and I believe some areas even require certain levels of training and possibly certificates to get on rotation but generally police rotation and cash calls are what you want to rely on, they pay the best and if you can keep yourself busy all day with just those two that is great otherwise you may have to look to motor clubs for extra work but again don't get too dependent on low rate motor clubs like AAA some pay good some pay not much at all, some are easy to work with some are a pain to work with, and motor clubs don't operate the same in different areas so someone in texas will have very different experiences with the same motor clubs for example Agero than someone in Ohio, or maybe even city to city where Agero might be great in one area they could be terrible in another so that is something that will be determined with personal experiences.
Now I've gone a bit into the cost barrier, the type of work you want to focus on, and the importance of building hands on experience, As for insurance and other business related topics I don't deal with truck insurance or anything like that personally so I can't speak on or give any insight into what your best options are there just build experience learn anything and everything you can.
Best of luck, and thank you for your service.