You have a blank slate which is great because you could do anything with it. I’d think about what you want to use the patio and backyard for - entertaining, kids playing, if you have pets, etc - as that can and should guide what you decide to do with the space. Googling to see what you like is helpful and here’s a few ideas to get you started.

I hope you mean you plan on painting the siding and trim white, and not the brick. Right now your brick is low/no maintenance. If you paint it, you can never go back to plain brick, it will never clean back down to plain brick, and you will always have to keep up on painting/maintaining it to keep it painted.

But you do have a great blank slate back there. What is your lifestyle? Hanging out, gardening, got kids, want to entertain... what kind of seasons do you have?

You could do a full porch along the back, roofed or pergola topping. You could build in a brick or concrete slab and add in outdoor cooking and living. If you have kids you can add in things that are kid friendly. If you have dogs or other outdoor pets, you can plan in for that too.