I included things from college that I thought were relevant to the overall image/story/brand I was putting together through my app. What's your image/story/brand? (Don't actually have to answer here if you don't want, but you have to answer that for yourself).
I think military service would look good anywhere. If by "significant EMT work" you mean training others or any other scenario where people worked under you or really anything beyond just "lots of EMT hours" I could see it being good for any specialty. If it's just "lots of EMT hours" then I think it's somewhat specialty specific as to whether or not you include it.