If you want to stay with one employer for your entire career, I would go with municipal. With municipal, you can typically get a DB (pension), or a DB/DC hybrid at the least (half pension, half 457). Most privates are only 403b or 401k. Just look through this forum, there are many posts about privates - who's losing a contract, who's getting taken over, who is losing part of their business to the local FD. How would you like to spend 14 years in a company then suddenly be forced to look for a new employer and/or be forced to relocate, perhaps out-of-state? A company can always be forced to relocate, or can go out of business altogether. For example, anyone who worked in NYC EMS for Cabrini, the SVCMC chain, or Victory Hospital had to look for new jobs. A 401k or 403b is portable, so if you don't mind moving far away for another job, employer stability may not be an issue for you. Just start putting away at least 10% of your pay 100% in equities from day one, and you should be okay for retirement in 35-40 yrs. Definitely don't wait to start aggressively funding a 401k/403b if that's they way you're looking to go instead of a municipal employer.
Having said that, some privates and hospitals can provide better schedules and other working conditions than a municipal employer, and in some cases better pay and medical benefits. If you're doing EMS as a temporary thing while you go for a degree, or even if you want to get a degree to climb the corporate ladder in EMS, your best bet is working for hospital-based EMS, as they're more apt to assist people with schedule changes to accommodate a class schedule. Second would be the privates, and the worst would be municipal. A rotating schedule, whole shift holdovers, mandatory recalls and having to be on-call can quickly derail and educational aspirations, unless you're doing something that is mostly distance learning.