Hello Zachary!
Paying down that student loan debt is very important for sure and may become an issue when you complete your mortgage application (due to your debt to income ratio) but if you can get approved and achieve a better rate of return than 4% on your property, it sounds like you're in the clear. Your knowledge of FHA looks to be right on point. It's a 3.5% down so it's a low cost of entry but, like you said, that also means less equity. You are also correct about refinancing out of PMI at 20%. The only other downside about using an FHA loan is that the property will need to qualify per the FHA standards. So only on 4 or less units and for FHA it is supposed to be your primary residence but it sounds like that's the plan already.
I know of people in the past who have bought duplexes or large single family residences then rented out rooms that have worked this strategy successfully in the past. In fact, the guy who bought the SFR and rented the rooms bought his with a VA loan ($0 down) back in 2012, rented out the rooms which paid his mortgage every month, and now has bought the house next door and rents the first house for nearly double the mortgage payment.
Because you are putting less down, and financing more of the purchase price (which means you are also paying interest on that money) your numbers won't look as good as they would with a larger down payment but it's not a HUGE amount. Roughly speaking, every $10,000 of financed money costs about $65/month, depending on your interest rate. How long do you plan to live there? If you buy at retail, you may not be able to cover the entire cost of the mortgage from the rental income at first but the longer you stay there, the more rents will go up and eventually you occupying a space there will be costing you potential rent money. (when you can rent if for more than what you are saving)
