I don't cut all my CS into ready made bases, even though 95% of the time I use the same size card base.
I have my full sheet CS stored in a filing cabinet right beside on my left. PIC 1. 95% of the time I only use SU! CS as this eliminates the need to figure out how to fit something in and keeps my system fairly uniform. The other 5%, usually 12x12, is stored seperately in a set of drawers.
My off cuts are stored in four, expanding 12-slot carry files, which is beside me on my left, in colour families. PIC 2. When I go to make a card I'll first look in them to see if I have a half sheet to use as a base. If not, I'll just cut into a new sheet. These are also very handy to throw a couple of extra full sheets into and take away with me on club days.
I store all my offcuts as 'squared off' cuts. PIC 3. What I mean by that is, I'll cut any off cuts down so they all have straight sides. So there are no scraps with hole shapes cut from dies or punches as I find these get snagged when stored together.
I also 'store' my rubbish scraps. PIC 4. I have a box under the desk for all the scraps I don't want to keep. I'll go thru it every now and then and fish out something that will be useful for something I may be working on. Every month or two I take the box and give it to someone working with kids as they find that scrap box a treasure trove of great collage material.