Is an FHA Loan realistic for me?

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I'm a single 32 y-o with a full time job living in Los Angeles. I was a freelancer up until one year ago. Now for the past year I've been working for a company full-time, and my NET annual income is about $36000. As of now I only have around $2000 in savings (thanks to some costly life events and high LA rent!)

I have good credit, around 760, and a full time job, but my salary is low. I never thought I'd ever be able to buy a home, but now I've just learned about FHA loans and I'm so excited about this new prospect of being able to buy a piece of real estate and stop burning my money on rent every month!! My question is though, is my low salary going to prevent me from getting an FHA loan? I'd also have to get creative for how to come up with the 3.5% but I'm not even at that point yet. I'm just trying to figure out if I could even get a loan like this first.

I would be interested in buying a duplex, triplex or fourplex and living in one for the first year. And then after that, perhaps repeating the process. I'd really like to build a portfolio. I'm very interested in owning multiple properties and generating as much passive income as possible. Of course the idea of being able to live with cheap/free rent while someone else is paying my mortgage is so great in itself too. 

I'm still learning real estate math (I also work as a property manager at a commercial real estate firm so I have some knowledge on bookkeeping, etc) but I'm not good enough yet to determine if getting an FHA loan to get a $1,000,000 fourplex in Los Angeles (or surrounding area) is going to kill me. The rule that says you shouldn't take out a loan that's more than 3x your annual income makes me think it's not even possible for me since my income is so low. But does that only apply if you're buying a single family home to live in or does it apply to a multi-family that you want to live in too?

Since I'd have to live in the property, it kind of restricts how far away from LA I can buy. I also don't want to buy something cheap in a bad part of town and have to fear for my life. This makes things a little harder as well.

If anyone has any input on my situation that would be great - is this realistic for me? Do I have a way to somehow get property that I could live in and have it be at least $100 cash flow positive?