I would be using the equity to purchase a new house for myself and my parents (they’re older now and need help)

The Cosigner Agreement states they are financially responsible, all communication will take place through the actual occupants, I don't deal with helicopter parents, they are responsible for payment of rent as well as any cleaning/repairs after termination, etc.Don't forget it's not easy to sue a cosigner if they live in another county.  

My parents conditioned me to be a great saver, but saving will not lead to financial independence in most cases.Once I understood my relationship, and used the savings to invest in an asset to pay for an event, everything changed.

Sometimes they also have a car payment or child support payments or major credit card debt. 

But if you are committed to purchase, a 2/2 would prevail over a 2/1, the price difference has to be nominal and now you might attract a different user like tow couples or adult friends that don't want to share a bathroom vs a young family that the kids are okay to use the same bathroom as the parents. 

It takes money to invest, so spend this time working hard and saving like a mad man while living off your parents for free.Educate.

So my parents are buying my first fixer upper for me all cash in there name. 

They were the "problem child" performers for me and all in one geographical area.

Case workers look at things such as disability, are the potential tenants collecting food stamps, child support, do they have other income, SS, how many children, what ages are the children etc etc etc.....In your earlier comment you said average for 3bedroom is around $900.

But our second child was due in May and we had a toddler now sans childcare.