Do I have to hire a professional, or I just become one?

I'm curious if I should hire someone in the NYC area so we can meet face-to-face OR hire someone in Austin who is more familiar with Texas real estate law?

Just hire one, even if it becomes a sunk cost I guarantee you'll learn a ton about mold that will benefit you greatly in the future. 

We noticed how very inexpensive it is to purchase there, yet the cost of living very high.We spoke to a relative who lives over there who also rents out a place and hires a property managing firm that ensures the rent is paid and all is in good condition at a very reasonable rate.

The cost of other (non-new construction) houses in the neighborhood have no relationship to the cost you'll incur to build a new house.Your costs will be based on a lot of factors:- Location- Level/type of finishes- Style of house- Size of house- Whether you GC it yourself or hire a builder- The types of contractors you use- Your negotiating ability- How strategic you are with your designs to keep costs downI've built houses for $60/sf, and I've built similar houses in other locations with different contractors for $90/sf. 

Of course we will hire an inspector if we go to contract, but what things should I be looking out for to save our partnership the time and effort of a contract gone south should problems arise. 

I've hired a company for this credit issue but just wanted to see if there are any other options out there 

If it isn't insanely costly - you might want to hire a property management company. 

Had to go outside for some fresh air during their pitch at our REIA a couple of years ago.

I'm currently active duty Air Force and recently returned from a deployment so I have a good starting fund for some investing.