If you want an ambulance job, most places require:
CA Driver License
CA EMT card
Ambulance Driver Certificate
Medical Examiner Card
AHA CPR for Healthcare Provider
To get your CA EMT card initially, you'll need to be certified by the NREMT.
Like Achilles said, ICS 100, ICS 200, and NIMS 700 would look good. In fact, that's the bare minimum for most ambulance companies where I live. Please search the forum to find out about how to get these certs.
I'd like to add that becoming an EMT is expensive, and depending what part of CA you plan to work in, your only options might be interfacility transport (IFT), not 911, which is not what most people expect. The pay is not as high as what people imagine, average I'd say is about $10/hour, but it could be lower or higher in some places. There aren't a lot of jobs either; it might take you a really long time to get a job. I got my first EMT job 13 months after I had all of my certifications that were required to work, and I've been working as an EMT for about 1 1/2 year for IFT-only companies. I have never responded to a 911 call.
If you have more than 2 points on your driving record within the past 3 years, an accident, suspension, or a DUI within the past 7 years I think, a misdemeanor, or a felony, some variation of these, don't even bother.
Since jobs are limited, scheduling isn't great either. If you aren't available to work whenever for these ambulance companies, they might not hire you, or keep you. This could really limit your time with your friends and family, or make going to school difficult if you plan on earning a degree.
Before I became an EMT, I imagined the "paramedics" in the ambulance were like doctors (I called everyone in the ambulance a paramedic). I thought they learned a lot, they could do a lot, and that had lots of experience. I don't mean to bash on EMTs and Paramedics, but this is usually not true. At the time I went to school for EMT, CA required EMTs to take a class for 110 hours with one 10 hire ride along. My program went above and beyond and was 118 hours long with one 12 hour ride along. I think they require more now, but I haven't kept up with the changes if any. Hopefully this demonstrates that we don't go through a lot of schooling, and I'd like to add that EMTs cannot do a lot of things like administer drugs (in CA, usually supplemental oxygen and oral glucose is all we can administer), we cannot perform procedures or diagnostics like start an IV, intubate a patient, cardiac monitoring, pulse oximetry, or check their blood glucose level. I am very dissatisfied as an EMT by how little we know and how little we can do for our patients, and I feel like a phony everytime I interact with the public and have a patient because they expect so much out of me.
Had I known this before, I probably wouldn't have started. I am very dissatisfied as an EMT. I'm going to paramedic school, kinda seeing where this is taking me, I am pretty enthusiastic about it too, I will be able to do more for my patient once I get a job as a paramedic, but I also need to keep in mind that there are almost no paramedic jobs out there, I still might not work on a 911 unit, and if I move to work as a paramedic somewhere else, I will probably get not much more than an EMT.
If you still want to do this, rock on.