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You need Licensed Plumber, electrician, hvac guys that can pass an inspection and pull permits to be legit.

Is data from the city on permits issued one way to find out?

Since Im mainly involved on the financing end I would look at the after repair value (ARV) of the construction, permits/softcosts, holding costs, land acquisition costs, and etc to make sure you have sufficient margin or safety for profit if you need to sell or equity if you need to refinance or take out that construction loan so you can hold.I would always recommend multiple exit strategies prepared in advance so you arent forced to take any specific route.Generally Land acquisition costs are 10-20% of project cost but in areas where the ARV is 300-400 persqft or higher you can pay a higher cost for land and still make your intended equity creation (if you intend to refi) or profit margin (if you intend to sell). 

A little bit about myself: well outside of work, I enjoy rock climbing, generally being outside, and playing recreational sports.  

We wish to maintain control of our ability to operate short term furnisehd rentals, so, we will avoid properties with COAs/HOAs unless they expressly permit this activity and are friendly toward operators.

You might want to agree to appoint a neutral to arbitrate any dispute.Also, if you think that you might want to own your piece through an individual LLC or trust someday, make sure that the language of your LLC agreement permits a transfer to a related entity whenever you want to do so.

What permits or licenses should I consider when doing my own rehab work?

It is less in the older homes as many of them were previously updated.Something that I like to do when researching Indianapolis (Marion County) homes is to do a permit history search for both the home in question and the homes in the immediate area.

You may need to identify significantly more like-kind replacement properties than the first two identification rules permit.