Due diligence advice needed, had my 1st offer accepted

[Noel R.]

Been listening to podcasts and surfing the forums for years now. Finally found an off market deal where the numbers are tight but it works for my long term goals. 

Duplex with 3/2 on each side and 1 car garage. New roof going on as I type with current rents at $1000 but market rent is $1300-$1400. 

Found the deal by picking up the phone and talking to an agent about a current listing.

Best part is offer was accepted at $290K and an identical unit just hit the MLS at $360K.

Now the due diligence begins. Working with a realtor, but any and all advice greatly appreciated.