My question is the following, if I buy an investment property (while continuing to rent where I live), does that prevent me from qualifying for an FHA loan later on when looking to own my primary residence?

Even when house hunting for my residence a house would be gone within days of being listed. 

I'm talking about for my personal residence by the way, just in case I didn't make that clear.

Phoenix's Maricopa county grew the fastest last year with over 78,000 new residents.   

My friend has one on her primary residence and has used it 3 times since purchasing without much hassle.

Take a HELOC and house hack a 2, 3, or 4 unit with only 5% down as your primary residence.

I am in the process of closing on a primary residence through conventional financing.I have a unsecured line of credit, that i occasionally move money into my main checking account, when I pay contractors for work on rentals etc. 

I will have a conventional loan on the property  and will be on paper used as a second residence.

Scenario 1 (HELOC on conventional): You will be able to get more on it as it is your primary residence.

Hopefully I can find an agent that can help with our primary residence now and then a rental property down the road.