FHA Loans on Multi-Family Properties

[Trey Gartner]

First-time poster and general REI noob here.

I recently went through the process of getting pre-approved from one of the many online loan sites. The initial approval was for $450,000 with just under $25,000 as a down payment (worked out to about 5%). The next day, I received a call from a loan advisor at the bank I currently have my money with. When digging into the weeds he told me a few things, one of which gave me pause: 

1 - My initial approval was based on the purchase of a single-family home, and would not include 2-4 unit properties.
2 - In order to get a conventional loan on a 3 or 4 unit property (my ideal purchase), I need to put at least 25% down. 

3 - MOST big banks down write FHA loans for purchases of 3 or 4 unit properties, regardless of your intent to live in one of the units.

That third point seemed a little general for my liking so I thought I'd pose this question to y'all. Is it difficult to secure an FHA loan for 3-4 unit properties? My credit score sits around 760 and I have over $200,000 in the bank while making $90,000/year, so I doubt I'm considered "high-risk."

Bonus Question: Is it better to put down the 25% upfront and go the conventional loan route or take on an FHA loan @3.5%-5% and keep the extra cash for future investments? My gut tells me cash and liquidity is ideal, however at what point does PMI and higher rates eat up the benefit of having more cash on hand?