I use a tackle box for my "computer tools" and it has a large assortment of screwdrivers and hex keys (including two sets of precision screwdrivers), pliers, wire cutters, a small wonderbar, bunches of screws and fasteners, zipties, cotton swabs, a VMM (and gator clips to go with it), a few spools or scraps of wire, markers, pencils, and pens, a small tape measure, a small level, a calculator, electrical tape, tweezers, a screw/socket extractor, thermal paste syringes, cannisters to hold screws/ICs/etc as they're extracted, a multitool, and various crimpers and strippers.
It's the end-result of a few different "computer tool kits," a few different screwdriver/pliers kits, and specialized tools that I've picked up over the years, all into one box. I've got 12 ft of glow-in-the-dark fish stix in their own case (way too long for a tackle box) along with attachments as well; they make pulling wire much easier in some circumstances. I have a closet that has sorted rubbermaid bins for all of the assorted cables and hardware, as well as spare anti-static bags.
Someday it'd be nice to have a mechanic's toolbox with the drawers for all of the various stuff, and organize different types of tools into it, so there's a drawer for screwdrivers, a drawer for pliers, etc, but those boxes are fairly heavy and can be kind of expensive.
Gas dusters is kept just kind of "around" but a vacuum sometimes works too. As far as the compressor - I've always been told that's a very bad idea, because compressors usually contain a reasonable amount of water (if you've ever worked with one and had to drain it, you know what I'm talking about) and can also generate a static charge, which may cause damage to various components. Canned "air" is not actually air at all, its often a flourocarbon gas. Vacuum cleaners with hose attachments can work as long as you're careful with the hose end (they're often metal) - ideally pull the heatsink off and vacuum it out, although if you can remove the heatsink I'd say just rinse it out in the sink with water; no dust in the air, and it'll usually clean it more thoroughly.