In my experience working and "playing around" with electronics actual ESD damage has been rare. I MIGHT have zapped a CMOS chip many years ago (it never worked so it may have been DOA) and I had an Arduino "go bad" for unknown reasons and that MIGHT have been ESD. It's good to be careful but I'm not THAT paranoid about it!
At home, I usually leave the parts in their original packaging. Otherwise I'm not that careful... I just touch-ground before touching components or circuitry. I don't use a ground strap and I don't have a grounded work surface. It probably makes a difference where you live (humidity) and other environmental factors (static-generating shoes/carpet, etc.).
At work, we DO have strict procedures. We have ground straps that have to be tested every day (wrist straps or shoe-straps, or I actually have ESD conductive shoes). Work surfaces are static-safe and tested periodically and the floors have conductive floor wax, etc.
I've worked in places that were less strict. Every place I've worked has had grounded workstations and ground straps, but we didn't always wear the wrist straps, etc. Once, I actually had a "static generating" chair at my workbench and I would often get a spark when I touched ground. That's BAD and I certainly COULD zap a component/board but it never actually happened.
I've used the old anti-static bags from other components to add a little liner to the bottom of the storage compartments
That should help as long as it's a conductive/shielding bag (black or sliver). The pink "anti static" bags don't generate static (so they are much safer than regular clear bags) but they don't provide any actual protection.
Our rules at work say components have to be completely enclosed in a static shielding bag or be stored/transported in some other enclosed shielding container.
But, I worked at a company where we stored "master" EPROMs in regular clear parts drawers and we never had a problem.
I'd rather not store things like 2N2222
Bipolar transistors (and diodes) aren't that sensitive. They can be damaged, but I'd be more worried about CMOS, FETs, MOSFETs, etc.