Do I Need to Re-build my Rental History (Property Managers and Real Estate Agents)?

When I was 24 I moved out on my own for the first time. I moved into a rental home, without an issue, when I did not renew the lease. I stayed in another rental townhouse for 3 years, but left prior to the eviction, after the birth of my son. Currently I am staying with my family and not paying rent, due to the illness of our mother. I want to rent again; however, I began to wonder if I need to re-establish my rental history. Having the deposit and first months rent is not the issue, getting what I want is. My goal is to move into a Rent to Own and move forward to owning my own home. This way I can save my money, payoff old student loans, and when ready, move into a home, get a feel for the neighborhood, before taking the plunge to home ownership. Is my plan sound?