Just filed 2019 but not 2018 what happens next for stimulus

The stimulus will be based on either 2019 or 2018.  If you didn't have to file the 2018 return, there is no need to do it now.

The question is how does me filing my 2019 return today signal the stimulus payment to process and what could be the estimated time frame. I had not filed 2018 or 2019 prior to today. And filed 2019 only today.

Once your return has been accepted then you will be set to receive the stimulus payment. If you have included your banking information and chosen to receive your tax refund via direct deposit your stimulus check will also be directly deposited. The estimated time frame cannot be determined at this point. The IRS is the one processing the stimulus payments and the final announcement of a payment date has not been announced. Please view this IRS link to stay up to date on the latest information.

What if I was supposed to file in 2018, did not file, owe back taxes, and filed for 2019 with a payment plan?

Since you filed a return for 2019 and if you meet the income qualifications you will receive a stimulus payment based on information in that return.  Here is a link with more information on the program.  You can check the status of your payment here.