Looking to "House Hack" with an FHA loan

[Patrick Carpenter]

I am currently renting an apartment for $575 per month and I pay the electric bill. I found a house for sale (60k) that includes a garage apartment. The garage apartment is currently occupied and the tenant pays $500 per month and his own utilities. I am approved for an FHA loan and am considering purchasing this property. The $500 a month rental would nearly cover my mortgage so I would be living in the house for free. The house is in decent shape, but needs some cleaning and TLC.

Is this a good deal for my first purchase? 

Any information or tips would be greatly appreciated.