You should start analyzing as many deals as you possibly can, even if you know they're no good. Do at least a couple hundred of these over the next few months so you can really get comfortable with what a good deal is in your area. You should be able to see a newly listed 3-plex for $xxx.xx and know right away whether it's a potential deal or just garbage.
I started out in real estate with no experience, and in the 6.5 years since buying my first duplex I've analyzed thousands of properties and have a total of 35 units and a self-storage facility. I know every street in my city along with rents by neighborhood, and can tell within 2 seconds of a property being listed whether or not it's worth a second look. I'm sure a lot of other people on here can do the same which should show how important it is.
Don't get ahead of yourself and spend this year really educating yourself on what a good deal is in your area and surrounding areas. Even if you're not interested in those surrounding areas it's all about the analytical experience. You should know the approximate monthly utilities cost for a duplex or 3-plex if not separately metered, how your purchase may or may not have an effect on the property tax bill the following year, etc. The often-forgotten details can add up make an ok deal a bad deal very quickly.
Last, there are other low-down payment programs besides FHA. If you go 203k that's another story, but meet with a lender to discuss other options which won't require a refi to get rid of PMI. Also, I don't know about your market but with how fast homes are selling here a FHA offer is not very attractive to sellers because the property condition requirements are so stringent and they don't want to deal with headaches when they have 10 other offers.
Feel free to reach out with any questions, I know if I had someone with experience to talk to when I first started I'd be much further along than I am now.