I'm lucky...I have a whole room dedicated to my collection of over 1300 sets.
I keep them all in their original boxes and the instructions in a seperate folder in theme order. The parts of each set are stored in zip-lock bags of various sizes, in the original box, and then in clear plastic 'reallyusefulboxes'. The vast majority of plastic boxes are the 84 litre ones and then the 145 litre boxes for the large sets (school, 1900 mansion etc). I cannot separate the sets into theme order in the plastic boxes as it would take too much space...the sets are simply stored in 'best-fit' order.
My storage system would not suit you by the sound of it as you don't want to keep the boxes but I would still recommend 'reallyusefulboxes' as they are very sturdy and stack easily...plus, being clear plastic it's easy to see what is in that box.
Claire