Your agency will probably be most interested in your ability to respond to serious trauma like gunshot wounds, knife wounds, care accidents, falls, etc. The reality is that you will not see this stuff regularly unless you work in a busy EMS system in a bad neighborhood. Working EMS will give you a lot of well rounded experience, and you’ll probably be of more help by treating tons of dehydration between 4th of July parades and St Patty’s Day than you will by treating Gunshot wounds.
But...your agency would probably still value the treatment of GSW’s much higher, despite the fact that they won’t see that every day, and you won’t see that every day in EMS.
If I were in your shoes, I would take ITLS or PHTLS every year, and I would take TCCC, TECC and LEFR-TCC as often as possible until you master the material. Then, I’d get hooked up with someone who teaches TCCC and start teaching. If you master this material and teach it every day, you will use it far more than a full-time EMS employee that uses it once a year or less.
I’ve treated two GSW’s in 7 years. How does that make me an expert? It doesn’t. It’s almost the same as having zero experience.
I’d also get an EMS job that is fun and 1-2 days a month. Something that you can get some limited experience with basic care, since people will look to ask you questions about basic care. Maybe do something like Event Medics.
TL;DR: dedicate yourself to TCCC and get a very limited job doing something basic.