Honestly, there is a zero chance you'll get approved for a mortgage in this situation. Literally zero. First time buyers will almost never get approved for an investment purchase, and an out of state first time investment buyer with no assets outside their down payment will probably get laughed out of the bank.
As for going FHA... the premiums are absurd and damn near impossible to get rid of. Not to mention that buying a property as a primary residence with the intent to move out right away (or never occupy) is unethical and mortgage fraud. Also, if you have to consider FHA, you're not ready to buy a house.
I don't want to sound harsh, but this is a really unrealistic and risky goal. Finances aside, if you've never owned a home, you're not really in a good place to maintain a rental. And doing it through an agent from a distance... I have a hard time seeing how you'd turn a profit even if you did get approved. I'm pretty new to Mustachianism too, and the urge to jump in and get started is a strong one. Just don't make your first move a risky, difficult one. Buy some indexes and REIT's and let your 'stache build for a few years until you're ready to buy yourself a house and have the assets to do it. No need to jump into mortgage debt on the hope of some future return when you don't even have anything in the bank.