For most home stuff, a good quality multibit screwdriver is good. I have a few of these, including a pink one for the distaff side to use:

There are cheaper knock-offs but these ones have good quality hardened bits and they don't easily break or deform. Torx bits are useful for some appliances. You'll usually need Philips, flat blade and maybe Robertson.
There are all kinds of (more unusual) situations where this screwdriver won't work- it's too long, too fat, too short etc. For that you may need special screwdrivers that you can accumulate as required.
Other than a few situations such as small Philips screws or hose clamps, screwdrivers are not that useful for working on cars- most fasteners require sockets or wrenches.
Security bits will fit a driver such as the one shown or a 1/4" ratchet, however they generally come in two types- individual high quality bits sold by industrial distributors at eye-watering prices and poor quality sets with many bits. It's worth having one of the latter around for the times when you need need them, but they break easily. Even to fix a toy you may need a delta bit.
Here is a poor quality larger set I have:

For electronics, a 4mm magnetic bit set is good. That's a whole different subject and probably off-topic here, but having Apple pentalobe and JIS bits around is useful. Try to find something high quality with good reviews. Here is one that I've had for years (red box):

The 69-in one was a gift- can't speak to the value but the bits seem okay and there is a good variety of them. The electric drive is gimicky and I don't use it. The Swisstool is a screwdriver that is insulated and fits +/- terminal block screws. The Greenlee flat blade is solid. The Wera is a Philips with laser cut teeth that help getting stubborn screws out (it sort-of works).
Usually good quality bits are black on the business end, but sometimes you'll find poor quality bits that are black and still soft or brittle, or sometimes even just painted black (looking at you HDX/Home Despot).