If you store them well there shouldn't be any problems going over time. Well means flat and nice in a box with a lid and where they will stay pretty much undisturbed until time to go. You can sort into baggies too but they slip and slide around when you don't want them to, so keep them in a box with a lid! I write in Sharpie pen on the bag any notes I need, like number of pieces or whatever.
However, I prefer to do all of one stage at a time, so I would probably rough sew them here and there and then trim down all at a time, or at least do them in groups.
Are you using a consistent background fabric? That can make a difference in how you sort and store.
I work a lot of with scrappy quilts and have devised a number of techniques to achieve randomness. True randomness can result in ugly, what we want as quilters is aesthetic randomness. What I've learned over the years though is that no matter what you do, sooner or later those two fabrics you were trying to keep away from each other ends up hand in hand...
Usually I use a variation of what Karla Alexander describes in her Stack the Deck books. Basically I keep my identical fabrics together until I combine them the first time and then I just avoid having any matching fabrics each round of connections. So hard to describe but let's say I allow myself 8 units in a top, that means (for me) that I am going to want at least 10-12 different fabrics (minimum) in the stack. I would have one stack of red, one of light blue, one of yellow, etc. for 10-12 stacks. Then I'd take the red and match it with the light blue, the yellow, etc until the red is all gone. Then I'd add a new stack to the end of the row and starting with the light blue, I'd match it with the yellow, etc. You just keep rotating until you are done. When you do your next set of connections, you take the first one without a duplicate. I typically want to put together the fabrics I have the most of first, and then use the ones with only a couple of pieces at the end because otherwise you can get sort of stuck.
https://www.goodreads.com/book/show/...tack_the_Deck_
I've also used the paper bag technique for a crazy quilt. Recently I did a project where I really pushed myself to disregard all my usual rules and just go for it and I let all sorts of things happen that I wouldn't ordinarily do, like I wouldn't put a green stripe with a green polka dot, or a green polka dot with a purple polka dot. It came out fine even with stuff touching
