Power wash first and use concrete paint.
Painting concrete is a great way to update your home. I would go to Sherwin Williams and take a photo of the patio and ask their suggestion on paint.
There is special paint made just for concrete, we used it in our basement but there is also others for outdoors.
We did this to our front steps last year! We used outdoor paint. Here is the tutorial: https://www.aratariathome.com/blog/how-to-update-concrete-steps
Concrete paint. If doing sections I like to use spray paint.