Help me with a toolbox for socket set

Shop Craigs list, flag down a tool truck see if they have any used boxes taken in trade.

My track box is a plastic Stanley roll a round; rolls like a 2 wheeled hand truck; multiple drawers, removable trays, a tip out drawer, works great!

You stated you don't have a garage, so what ever you get should be mobile, in and out of the house/apartment, you don't want something too heavy to lift or move by yourself.

For years I worked out of a tote box, set up saw horses and ply wood to set my tools out, kinda crude but it works........you're not working flat rate
Been a professional tech for 30 years and honestly have never seen a smaller tool box than a mobile cart traded in and for sale , and they want silly money for everything ( don't get me wrong , as a professional I NEED snap on and Cornwell / matco ) harbor freight or northern tool have great choices for adequate tool storage .
Have you considered a mobile cart with storage and work surface and then if you need to go truly mobile ... Use modern tool bags , I certainly use them always ! They will handle way more weight than even some metal boxes .. Harbor freight also with those ... Cheap and I've never had one fail . Holds up as well as my snap on or crafts man bags . Years of abuse and over stuffing with all mine .
I don't know what your space is allowing but a cart / storage / surface combo from HF is not expensive and truly gives room to expand and the aforementioned socket rails and organizers fit and can be bolted if necessary . Just my take