That being said, you know your situation the best.

I'm in the same situation.  

Between the four of you, you make about $510,000/yr, which will qualify you for a sizable loan.

We are open to getting a home renovation loan and finding something cheaper and renovating, but we still can't get into the prime areas for the budget.We have been advised to make sure to choose an area insulated with good schools and parks but that's just not possible with our budget unless we go to the suburbs, which we are not willing to do.

You will get appreciation, loan amortization, and housing expense savings while you're there. 

Probably not the same situation. 

I wanted to create an open discussion for some experienced investors and understand what you would do in my situation.

I'm wondering what other types of creative financing or loan products might be available for my situation.

I'd start by talking to a mortgage broker/loan officer to find out how much you're qualified for. 

Look into ways to pay, like common loans, government-backed loans, or money from private people.