As soon as the paramedics or the firefighters walk in, they’re going to take stock of the situation. They’ll do it very quickly; you might not even notice it. They’ll look around and note the conditions of your home. They’ll look at your skin to see if you’re flushed or pale. They’ll notice whether your skin is dry or sweaty.
Before they ask the first question or set their equipment down next to you, they’ll know if you’re dangerously sick or if they have a few minutes to assess you some more. Regardless, you are in good hands now.
When it’s time to put you in the ambulance and take you to the emergency department, the decision of where to take you will be made through a combination of asking your preference and taking advantage of the strengths of each hospital. If you’re having a heart attack, for example, it makes sense to take you to a hospital with the ability to perform heart catheterization. The paramedics might even have protocols that dictate where they must go. Express your preferences, then work with them to figure out what’s best.