First of all, if your mom makes less than 30,000 a year, school will be virtually free because of financial aid. The rest can be put on debt and paid once college is complete. I recommend living with your mom for a year or so when you first start college. If that is not possible, go someplace with dorms, that will likely be covered by financial aid. Start a job now at a fast food restaurant or something and make your pay checks direct deposit. Do not spend any of the money in their unless ABSOLUTELY necessary. In a year I made over $5,000 from my job working 20 or so hours per week at $0.50 over minimum wage.
Start with applying for College or even just contact one that your looking to apply to, they'll be able to answer a lot of the expense questions for you and assistance programs.Student loans maybe your only option, they're currently the 2nd largest debt in america after mortgages. Don't worry your school will set up with plenty of debt :)
You have a plan to get a job as a EMT. Your only 16 so thats a good start. especially since its good resume building material.
When the time comes leave your pets, find a good home for them. I know you don't want to hear it, between work, school n social life how much time will you have. Pet are an anchor, might as well have kids.
Get a job in a restaurant is a good idea, made great money as a waiter but they might want you to be 18 to serve booze. But they'll have other positions as well and they're nights.
I wouldn't worry to much your only 16, worry about having fun!
Depending on your city it can be hard or impossible to live on your own from a min wage job. Typically the landlord will want proof of a regular income 3 X the monthly rent, you can see example rental rates on sites like Zillow.com
If you are not being forced to move out ,consider that living rent free is your last and best chance to further your education, there are 2 year technical degrees that can get you a good paying job.
speak with a guidance counselor at your school