Did my EMT with Christian NE. From my understanding, Christian NE is the only County/City 911 service that is not fire based. Gateway/Abbott (AMR) are primarily IFT with some mutual aid agreements for 911, but not their primary business.
You can't get into Christian NE without being a paramedic and they take BJC employees first. So, depending on what you'd want, I suggest getting a patient care tech job at a BJC facility while you get your license.
As far as the fire based services, you'll need to get selected into the academies and that is a points based system. It'll cost you 4K (for the county, I believe) to go through their academy and no job promises thereafter with fire.
I believe that St. Louis City EMS, while fire based, doesn't require their EMS resources to also work fire, so you can get in there. I believe there is a residency requirement if you end up working there, you'll have to show city residence by some period. There are openings, because they do chew people up. Underfunded, understaffed, and very overworked, but I bet an excellent way to build some serious experience.