first of all welcome back! I am not the neatest with my scraps though I use tons of scrap for scrappy quilts. I have no clue how I have come to have so many.
larger pieces I do my best to fold. Smaller pieces get put as is into my scrap bins. When one gets full I start another. When I am ready to start a scrappy project I dig in and pull pieces randomly so I have a completely scrappy look. For smaller pieces it does require that I do some pressing before I can cut into them but I am able to maintain the scrappy look I want in the project.
As others have mentioned there are many ways to sort or store your scraps so dig in and have some fun.
I even go through and cut square or strips to find them with ease for other projects. I also save anything larger the 1-1/2". You Just never never know.