The reality is that the tax impact and ability to take ANY losses (as Michael mentioned) is based on a number of factors that include whether or not it is a "separate dwelling unit".

EXAMPLE: college student living with parent(s).Regarding using child support - suggest you follow mortgage requirements:1) Need copy of divorce decree to determine ages of children, so you can confirm how long it will continue.2) Need proof of at least 3-6 months of actual payments, as too many deadbeat dads.

You could have sent him to collections and this would destroy his credit, which could impact his ability to purchase a home, qualify for a car loan, and possibly even cost him his job.

Personally I have never been a fan of pre-tax accounts (401Ks and IRAs) because I feel like they constrain my ability to invest in the assets I want, so another consideration you may have is to temporarily stop those investments to save faster for your house.

Despite them performing inline with rent projections and occupancy, their flaw was in a short-term rate cap without any ability to refinance.

In my experience, appraisals have one purpose, and it is NOT to determine the actual current value of the property. 

So...am I shooting myself in the foot if I buy an investment property now (out of state) to begin my real estate career, and lose out on the ability to use an FHA in LA down the road?

Their ability to help you is limited if you go after. 

Have bought, renovated, refinanced and sold rentals in my portfolio.Besides monthly cashflow, you can cashout refi every 5-10 years or when increasing rents support the ability to do so. 

Hide you money, drugs and valuables off site.If you do your own opens, do it for a couple of weekends.Once you have someone interested, you fill out a purchase & sale agreement, collect an EMD, open escrow, order title, verify ability to close with the buyer's lender.