I would rather take down all cash and have the most options when to sell or refi if ever.

Stocks again can diversify (and frankly I don't see the benefit in investing in real estate related stocks - there are much better options) Are there any tax benefits?

BTW, a lot also depends on which state you are in .Here in Texas, its much more landlord friendly than other areas.

FHA gets a bad rap because sellers and many agents think it's only for people who don't have the money so if I had 20 percent, but wanted to use FHA, I would present a proof of funds with my offer showing I have more money, but am using the FHA as a financial option so I can get an investment property as well somewhere else.

I was just telling my friend today that I'm getting multi-family, high performance, and relationship mentoring all in one package! 

Option A would allow me to keep it as a long term rental .

What if she lies and claims to have owned a home, or uses a friend's address instead of the rental address?"

fun comps and see if cashflows. if need help on financing, more than happy to discuss your options

Eliminate debt, establish a budget, and save.

If you have equity and decent credit, a conventional Fannie Mae HomeStyle (or the Freddie Mac version) would likely be the better option instead of an FHA 203k loan (which will require a 3rd party HUD consultant to oversee the deal in addition to having the contractor involved).