Like what the others said, you should try to schedule a ride-along with a local ambulance company to see if this field is for you. A lot of the bigger companies (R/M, AMR, etc.) would probably not let do you a ride-along (liability issues) unless you're enrolled in an EMT-B course (which your instructor/school will probably schedule for you). Try some of the "smaller" mom & pop transport businesses - they might be a bit more lenient to let you ride along.
Another route you can take, is volunteering at your local hospital. I know some of the smaller hospitals with Level II or Level III trauma centers are not as busy as others and will probably let you volunteer in the Emergency Department (there's probably some basic training/orientation involved). The ED is the best spot to volunteer if you're trying to decide whether or not you want to go into the EMS field. You'll see a lot of EMTs, Paramedics, and RNs - which is the group of people you will be dealing with in the EMS field (not to mention it will most likely be your domain outside of your ambulance). They might even let you in on the action! When I did my clinical experience at Pomerado Hospital's ED, I witnessed and assisted with patients with all sorts of problems (not sure if that's the proper word..). The doc even let me assist her with the stitching of a patient's lip. Basically, you don't want to be pushing wheelchairs around from department to department. Get in on where the action is, because those are the things you will see and do as an EMT.
As for the pay, I think we can all agree that EMT is not the greatest paying job in the world, especially in San Diego. At best, you'll see a few bucks over minimum wage, but most of the time it's around minimum wage, especially when you're new. If you've been with a company for years, you might see a higher paycheck. Or if you continue on to medic / nursing school, you'll definitely see a higher paycheck. A lot of people don't join to be an EMT for the money, they join for the experience.
Hours vary from company to company. Some companies will hire you part time, some will hire you for 8 hour shifts, and some will expect 12 hour shifts out of you. There are some companies that run 24 hours shifts as well.
Situation-wise, I'm sure no one is going to know what to do in critical situation without the training. This is what the EMT-B course is designed for, it teach you to recognize the difference from a medical to trauma. It will teach you what is an apparent life-threat versus a secondary injury. MOST of the time, you will be on a rig with another EMT, so you won't be alone (I think there will be too much liability with a single EMT on an ambulance in a urban setting). Even with fire departments, they usually staff a medic and a lot of the FFs are EMT certified.
There are plenty of EMT programs here in San Diego. I've always been an advocate for Community College programs as I think they're great bang for the buck. I took the EMT-B course at Miramar College (their training facility is right next to San Diego International Airport), and loved the program. It was affordable (estimate ~$600 for tuition, books, and uniforms), and the instructors truly cared about your education. They also have plenty of different schedules so you wouldn't have to quit your day job just yet. I was able to go to school full time (university student) during the day and attend my EMT classes at night. So if after volunteering, you're still on the fence about switching careers, keep your current job and take EMT classes that fit your schedule. That way, if you ever reconsider, you have a career to fall back on.
I must warn you, the EMS field is not for everyone. I've seen this first hand in my EMT-B class - we started with 40+ students, which dropped to about ~20 students by the final exam. My instructors told me this is the case with every class, every year. EMT is no medic school, but it certainly isn't a cake walk either.
So if you're worried about passing out when seeing blood, etc., go schedule a ride-along or get a volunteer gig at a hospital. It will definitely show you if EMS is a right field for you. If you have any other questions, feel free to ask! EMTLife is a great community!