Hey Jimmy, welcome to TLF, glad to have you here. It looks like you've in a perfect position to choose whatever type of grass you'd like to have in your lawn. There's definitely a few things working in your favor, as you can go with the grass type that works for your light situation, as well as your tool and time selection. There's definitely a lot of shade in that area, and depending on how much light opens up once you remove the trees, that might open up a few more options for you.
I'd recommend researching the grass type that you find would suit your needs, as we have users here that have shade tolerate types, as well as full sun types. Look through some of the lawn journals on the warm season lawn subforum to see what grass types might suit your situation.
When you're ready to renovate, take this advice: don't till the ground.