I cut out the project like you to ensure I have the fabric required. I assemble block units that can be chain pieced to save time.
I like to press the units at the same time. Next, I store the sewn units labeled in zip lock bags. Once I used the clear page saver sheets that go in a binder to organize the sewn block units. I work on different steps of a quilt pattern based on what time of day it is...mornings work best for me to cut and piece. Evenings are for pressing and pinning. Have fun!