Under table shelving can be very helpful. I built a shelf that spanned the whole bottom of the kitchen table to store paper for drawing, but it could just as well have been for books or low rectangular baskets of supplies. It hung down about five inches, but could have been lower- maybe 6 or 8 inches and accommodate a lot more. We have built a larger table now, but that 1st one is a work table for outdoors and the shelf underneath stores tools and supplies.
How big is the cabinet you have to work with? I couldn't fit everything into a standard kitchen cabinet, but we are building our own kitchen this winter and will have a floor-to-ceiling shelving unit with boxes and dividers to house all of our table-work stuff in the kitchen.
We live in a small home too (780 sq ft- up from 650 last year
), and floor-to-ceiling storage units are a must for us in every room. Everything is built-in as well so that we can use all of the otherwise 'dead' space.
Open shelving with lots of rectangular baskets works the best for us in most scenarios. In some cabinets, that would work as well, if you can move the shelving inside.