Hey Morgan, Welcome to Bigger Pockets! Sounds like you are in a awesome position to begin investing which is exciting! The hybrid house hacking strategy that you are shooting for may not be doable for FHA. I don't believe that you can do AirBnb with an FHA loan. They do not allow rentals that are less than 30 days...
However with a great deal and up-to-date market rents you can certainly still shoot for cash flow on a 4 unit while you live in one of the units.
I invest and live in Colorado and I think it's a great market! I have a property near a University and see quite a bit of multi-units with tons of potential. To answer your "what I would do" question I would certainly use my FHA loan to purchase a multi-unit , live in one unit and rent out the others to cash flow.
For your question on using the property as collateral you can certainly do this. As you pay down the principal and property continues to appreciate you will build equity and can leverage that equity to purchase more properties.
Happy Investing, feel free to reach out with questions!