Purchasing a 2 flat

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Hello everyone

My name is Alex and I am a contractor in Chicago area. I always thought about getting in the real estate but I'm always swamped with work so I didn't really have time to sit down and start reading more into it.

All these until my mother in-law had a family meeting with us and she told us that she can't manage all her properties anymore since she's over 60.

So she asked me if I want to buy one of her properties. Now, here's the deal she proposed and I need your help/advise in taking the decision of buying the property or not. 

The building it's a 2 flat situated in the Little Village area in Chicago IL. It's on Whipple St between Cermak and 26th St.  She asked 90k for the building (regular financing through the bank). I offered her 75k cash and she accepted under the following payment plan: 15k as downpayment and every 12 months 10k. 

There are 2 apartments, each 3BD 1Bath. 

One of the apartment is rented for $650/month to the same people for 27 years and they like the apartment and don't want to move anytime soon.

The other one is vacant but I think that I can make it look nice with 10k and rent it for at least $650 as well.

What do you think I should do? Should I buy it? Would this be a good first buy for me?

I'm waiting for your advice.