As you said, have them pay for the oil and i would have a " security deposit" of a full tank of oil added. just remember, they don't fill the tank and there is no heat in the house during the winter, guess what happens to your pipes and your house ?

I want to use a private lender/friend to fund the rehab, how much of the profit do they deserve? 

You can also find a lot of people who would be interested in partnering up and use private money instead of hard money lending.

@Elaine Brooks to follow up and expand on what @Soleila Gonzalez was asking; what kind of financing did you line up, Private money?

If so a secure 5-6% return might look pretty good. 

I am a private money lender.  

Since it's in Chicago you might wanna avoid security deposits and opt instead for a non-refundable move in fee

(By the way, We can use private money, but the cash flow takes a big hit.

Then you can control how the funds are invested and put them to work in real estate, private mortgages, etc. 

I want to locate a place I can call home, but also become very knowledgable so I can secure property to either rehab and rent or flip (make money).Don't need to get rich quick approach, rather solid practical ways to be successful!