I'm likely going to be a Trustee and I'm wondering if there is any financial advantage to my Dad creating a corporate entity and transferring the house to the company, and then the company to the Trust. 

One of the standard setup is to have each property in its own single member LLC in the state of the property.The property LLCs are then owned by a holding LLC in WY or NV to benefit from their good charging order protection.In addition, you would use a C corp as management corporation to take salary (if needed to show steady income for future loan approval), retierement, medical and other fringe benefit.

To pull a permit on a structure that you do not plan on living in for the 12 months after completion, or if the structure is owned by a corporation, LLC, etc, (not sure if they research this) then they would require you to have a licensed GC to pull the permits. 

I also went to undergraduate in PA and grad school in AZ, and in both locations large apartment complexes were being built, and the local landlords couldn't compete in one location because of over development by the large corporations.  

Get a logo on your car, post it on your social media- twitter, Facebook business page- that will also help with local searches, if your town has a BST page.

We have the location, hiring the staff, building out, etc. but with our corporate structure I'd like some advice. 

If a regarded entity owns it then the entity pays the tax and gives you a partnership or corporate return with the tax being paid.  

The landlord, or any person authorized to enter into a rental agreement on his or her behalf, shall disclose to the tenant in writing at or before the commencement of the tenancy: (a) The name and address of: (1) The persons authorized to manage the premises; (2) A person within this State authorized to act for and on behalf of the landlord for the purpose of service of process and receiving notices and demands; and (3) The principal or corporate owner.

Would it be good to make it as a living trust or under corporation to have enough for expenses and distribute rental income?

One particular strategy that interests me a great deal is short-term corporate rentals.