When I first bought my own equipment, I was clamping the press to an entertainment center (I had to be careful not to tip it over
). When not in use, everything got stored in a cupboard that measured about 13"H x 13"W x 18" deep.
It wasn't much "fun" but I was able to reload, when needed.
A popular option for limited space, is a Black and Decker or Craftsman "Workmate"
work benches. There are several sizes to choose from, and the Workmate folds for storage.