Once you pass 4 units, you move into commercial lending... a completely different set of mortgage guys/brokers in that world.
Yes, you can get in with less than 20% down. I believe a typical commercial loan will be at 65% LTV... but in the commercial world the lender may allow a seller carry back of some or all of the remaining 35% with a 2nd position loan/mortgage/lien.
Things to know about commercial loans... they'll have shorter amortization (generally 20 years versus 30 on residential)... higher interest rates (generally a full point higher)... will be variable versus fixed... and will likely have a balloon payment.
I don't know of any Florida realtors but you want to look for a commercial realtor. Do enough searches for commercial real estate and I'm sure you'll find a few who specialize in it down there, it's a very different market from residential.
I don't know of any first time buyers programs... you aren't investing with owner occupied as your competition, you're in a purely investment world in complexes.
Good luck keeping your payments low. You could accomplish that two ways... one would be to make a huge down payment... less financed, lower payment. The second would be to buy a severely depressed property. If you buy off a valuation from a $200,000 GOI and somehow turn it to $400,000 GOI, your mortgage is going to be smaller relative to the new income.
Personally, sounds like you're trying to run before you walk. I'd stay residential until you know what you are doing. You can buy a handful of 2 - 4 unit properties for the same $600k, can buy them in series so you don't need the full $120k down payment before purchasing the same one. You get far better financing terms with residential mortgages... and there's no real down side as a $600k complex won't be large enough to give you any real economy of scale. The 5 unit to 60 unit complexes are sort of no mans land... crappy terms but not large enough to get the economies of scale investors want.