Advice on first property/properties

[Jacob Bunce]

So, I'v been doing a lot of studying the last couple weeks, and have found a duplex that fits all of my qualifications (I have another thread about that one) and am going to attempt to get financed for this land. I had originally planned on using FHA and attempting a 'house hack' with it, however, I was wondering if another option would be better.

I found another house that seems like a good deal for a live-in flip. (or if we fall in love, just a good place to stay) The property is listed at 74k, and I plan on offering 60k for it. Most of the houses similar to this one in the neighborhood/area are at the 120,000 price point. The property also has a pool, which appears to be decommissioned, how-ever, my father-in-law has been a professional install/maintenance 'pool boy' for many years, and I myself have done many jobs with him. It would be quick and cheap to get the pool back into good shape. 

Is it possible to get the duplex using a conventional loan, then buy the house using a FHA loan? The time between buys would be roughly 3 months. I would be fixing this property up, and getting rid of the PMI ASAP. If this is an option, how long do most loans take to mature and allow the PMI to be dropped?