I spent over 20 years as a General Aviation A&P that was both flying and maintaining aircraft from a Piper J-3 Cub up to a Douglas DC-3. I was on the move a lot, and kept my tools in multiple Craftsman carry boxes. No box was heavier than I could carry by myself, and the largest was a 3-drawer model.
When I was spending time working in a hangar, I always was able to find a spot to put my boxes. A rolling cart with a piece of plywood for a top would have been a good choice for me when in the hanger. I kept my wrenches in a tool roll with grommets that I could hang from nails/screws from a wall, or roll up and put in a toolbox when moving. Often, in the field I would just unroll it on the ground.
I kept my tools separated by type in the various drawers, screwdrivers in one, pliers in another, etc.. I had one box for socket wrench sets, separated by drive size in each drawer. If you do this, it is easy to track your tools if you put them away at the end of the job. You don't need outline foam. Less used tools were spread in other boxes. I had one box for test gear, but the multi-meter stayed in the top of the main box because it was used often.
I used a small canvas (military-style) tool bag when working on a project away from the tool storage area. They are very handy when you don't need a big tool set for a specific job.
My experience was very different from airline work, so it really isn't very applicable, except when you need mobility.