What you can or can not use depends on which of the cutter models.
I was lucky enough to get a Studio model second hand, including several dies, cutting trays, and plastic to put over the fabric for cutting. All, I might add, at a very good price. However, a lot of the newer dies are not compatible with the Studio, so I have to be careful what I buy.
I use the big tray for small dies. It's easier than changing the trays out. I put the small dies near the end of the tray that goes into the rollers first, put a piece of their plastic over them and crank them through the Studio. That doesn't seem to cause any harm to the dies or the Studio.
If I had a ton of money to spare, I would by the electric cutter, the new model, and a zillion dies to go with it. But I can't justify that.