@Phillip Dixon There are a couple things to be aware of on an FHA loan. First, you've mentioned you're looking for 3+ units as the 2 families you've seen aren't cash flowing enough for your goals. But, 3-4 units have to meet what is known as the "self sufficiency" test meaning that the rents of 2 of the 3 units or 3 of the 4 units have to meet 100% of your monthly PITI payments. In the areas you've mentioned, there are very few properties that meet that cash flow. The one's you will find will likely need some type of rehab, which is where the FHA 203k renovation loan can be helpful.
Additionally, FHA can be a costly product. While its great that you can get in for 3.5% down payment, but there is also a funding fee (upfront mortgage insurance premium) of 1.75% of the loan value. Most of the 3-4 units in those cities referenced will start at about $750k. That will mean an extra $12,665 will need to be paid up front or added onto your loan balance.
Another drawback on the FHA loan is the monthly PMI is going to be extremely high. Typically its calculated at .85% of the loan balance, divided by 12 months and that will be your monthly PMI. When your loan exceeds a certain limit (I believe $625k) the PMI is calculated at an even higher rate. Your PMI could be in the $600/mo range. This PMI will stay with you for the life of the loan, so the only way to remove this would be to refinance - another expense.
Lastly, you'll be competing against other investors with 20%, 25%, 40%, all cash, etc. Typically sellers prefer those type of buyers over FHA due to fewer hurdles to jump through (ie. appraisal). In this type of market, buyers are paying premiums to use FHA loans.
All that being said, I'm a huge proponent of a first time buyer using an FHA loan cause I think its a great starting option. However, one should be aware of the possible negative effects they could have. I've worked with many buyers on FHA products for their first multi families. I've also worked with other buyers doing conventional and Mass Housing loans. My advice would be to speak with a few different lenders to see what they can offer you. Not every Lender or bank has the same products available to them.
One last thing, I am not a loan officer but I do try to stay as educated as I can on these products. I might not have all the information 100% correct, if not, feel free to chime in!