Buy a triplex with FHA vs build a nice duplex?

[Ellie Narie]

There's a triplex in my area that's listed for 289k (possibly could offer 275k according to RE agent), it has 2 one-bedroom units renting at $605 a month and 1 two-bedroom unit which I would move into if I were to buy this. The 605 a month seems low, because rents for one bedroom units are going for around $725-750 in my area, so I'm wondering if I can increase the rent, but then again, idk, the units aren't in too great of a shape (still livable though). 

The units look old, the carpet might need to be replaced. The two bedroom unit looks like it is in a lot better condition than the one bedroom units, so possibly the two bedroom might be ok without replacing carpets. If I were to buy this place, I would use FHA with 3.5% down.

Another option I've been researching is building. I've talked to a construction company in my area that builds duplexes. All in all, if I were to buy land for $65000, then the whole entire thing would cost $360000. Each unit would be a 3 bedroom 1.5 bathroom, with one bedroom and half bathroom downstairs and two  bedrooms and full bathroom upstairs. 

For a newly constructed 3 bedroom, I'd say the rents could be $1400 a month in my area. Maybe even higher. Also, the construction company says that there's a high chance that the duplex would appraise for 20% or higher than the cost to build it, a lot of their customers' homes have appraised 20% or higher, so that would mean I'd avoid mortgage insurance. 

What do you think? Just forget construction and buy the existing triplex, or do new construction? 

I want to be able to own multiple multi-family properties in the future, so I'm hoping that once I live in whatever property I decide to get for a year, I will move out and get another property. I heard that with an FHA it might be hard to refinance it unless I'd have at least 20% equity... What should I do?