Personally I would only invest if the a property hit the 1.5-2% rule.

Need to live in it for one year under FHA rules.

If this is the case, is there some reasonable rules of thumb to use here (e.g. how much should I be holding out for and what kind of a range in mortgage rates should I expect?)

Different states have different rules but in IL, ALL money exchanged must be disclosed to all parties at the closing.

I plan to apply for a personal mortgage and transfer that to our LLC once established.

This does not exceed the maximum rules for FHA credits.

Same rule here: the more victims it sees, the higher the likelihood that the AG would do something.I don't know how many active projects he and his company has going on.

@Jay Hinrichs I admit I increased my vocabulary looking up definition of hoary,  meaning old, white or ancient... but point well put and found way to Howey test (1946) for securities is broad and can be applied to  JV's, LLC and general partnerships As such, those being a sponsor of agreements should have proper legal counsel to advise them appropriately with caution,  as mentioned its all great until it doesn't go right and money is lost. 

Also, a good rule of thumb for expenses is 50% of rental income.

You just have to make sure that your property is rented and meets the 1.2 debt service coverage ratio with the rental income it brings before you apply for the refi.I am assuming you are planning to buy with your own cash or some form of short term private financing.