OK, so you will get many people's opinions on what do to, and some people (like the poster above me) are generalizing, and are wrong.
Lets start with the basics: you just got your EMT card; congrats. now get a job on an ambulance, if that is what you want. Believe it or not, many people get their EMT certificaiton with no intention of ever working on an ambulance.
Where are you? your location makes a huge difference as to what options you have available to you. If you are in SoCal, where FD runs the 911 system, your odds of getting hired on a 911 truck are slim. If you are in NJ, or anywhere else where it's a tiered system, your chances improve.
Also, if your system runs all 911 trucks as dual paramedic trucks, the odds of you getting hired as an EMT are 0; that's just how it is. So you need to decide on what you want to do.
Commercial / for profit ambulance companies are where many people start. they pay crap, often treat their employees like replaceable people, and are a stepping stone until you can go somewhere better. You might do 911, you might do IFT, you might do CCT, you might do nursing home 911, it all depends on what that particular place does.
Now, should you volunteer somewhere? I say absolutely.
@hometownmedic5 might disagree, but I will address all 5 of the points that were made:
one, money. yes, you won't make any money. you will gain experience, you will meet others in the industry, and you will learn how things are done. so while yes, you won't get a paycheck, you will gain stuff that will benefit you in your career. And you don't need to buy all that equipment; in fact, most volunteer agencies will provide you with the stuff that you need to do the job.
two, experience. my first volunteer EMS agency ran 4000-5000 calls a year, between 2 ambulances 24/7. I can also tell you that I've have busier volunteer shift than paid shifts, where often I didn't turn a wheel during a 12 hour shift; at my volunteer agency, I usually got at least 3 calls, and up to 8 calls in a 12 hour shift. We had set shifts, and recalls for any time the on duty crew was on a call. You didn't leave your job for calls, but if you are on shift on a night shift, or weekend, you typically weren't working.
three, sure, if you don't have assigned crews, and it's always a scramble. most agencies stopped that in the 90s. I'm sure they still exist, but more places are setting up duty crews so you don't have 40 people responding or being alerted for every call at 3am.
four: while most calls are taxi rides (and it's even worse in the cities), I've had more than my share of sick patients. the more calls you go on, the more sick patients you will see. doesn't matter if your paid or volunteer.
five: tiered systems do exist. it all goes back to where you are located, and what opportunities there are for you in your area. I can tell you if you are not in an area that lets EMTs do 911 calls, than you won't be able to do it. So you would either have to relocate to an area that does, or accept that you can't do 911 as an EMT.
Here the bottom line: like with almost all jobs, the more experience you have, the better the job you can get. you won't get a great job, but having experience significantly increases your changes of getting hired at the good jobs. In my entire career, there has been only one EMS job that I ever interviewed for that I didn't get, and it was a IFT job for a ****ty company. I did get the PT 911 job that I applied for a few months later. Few places want to hire newbies, many providers don't want to work with a newbie (except FTOs, who ask to train new people). That's how it is.
If you want a good job in EMS, you need experience, and the only way to get experience is by getting on the truck. Accept the volunteer job to gain some 911 experience, and if offered accept the commercial ambulance job to make some money and learn how the IFT system works, as well as to learn what it's like to work for an EMS company. I know my volunteer experience helped me gain my first and second 911 jobs (I was only at the first one for about a year, before getting hired at the second, much larger and better paying one for the for the hospital).
In my career, I've been a volunteer 911 EMT, a paid IFT EMT, a paid 911 EMT, a paid 911 EMS dispatcher, a paid IFT dispatcher and I can say that every job I was in gave me experience to help me elsewhere in my EMS career. But everyone starts somewhere, and getting that first job is usually the hardest.