You need a few screwdrivers.
Most everything in your house is held together with screws. Almost all of them are probably Phillips-head screws.
Philips screwdrivers come in numbered sizes. You probably need a #1 and a #2 to start with. Use a too-small driver and you can wreck the screw. Use a too-large driver and it probably won’t fit into the screw and if it does you’ll wreck the screw. Phillips screws and drivers are designed so that if you are in danger of stripping out the screw the driver will slip out of the hole instead. If you lean on it to get more leverage, you defeat that safety feature. And probably wreck the screw.
Despite their ubiquity, I kind of hate Phillips screws. The default almost always seems to be “wreck the screw”, and I too often seem to find myself with a screw that is half-in the wood and won’t go in or out. But they are everywhere, and you need to deal with them. Get a #1 and a #2 Phillips driver.
You’ll probably need a slotted (“flat”, “regular”, etc.) screwdriver, especially if you live in an older house or are doing electrical work: The screws that hold a switch or outlet into the box, and the screws that hold the cover plate on, and the screws that hold the wires to those devices, are almost always slotted.
I find I can get most slotted-screw work done with a 3/16″ screwdriver (coincidentally exactly the size of electrical plate screws). For much larger screws of course you need a larger one and for very small work you need a smaller one. Careful: it’s much easier with slotted screwdrivers to apply too much force and wreck the screw, and using a comically-wrong-sized driver will wreck the screw in an instant.
Some thoughts about screwdrivers in general:
The handle should be comfortable in your hand. large enough to naturally fill your fist. It should not be smooth and round; it should have sides, so the palm of your hand has something to work against to apply leverage.
The part the touches the screw should be carefully-made, and of metal hard enough that you will wreck the screw, not the screwdriver. Most screwdrivers (both slotted and Phillips) flare out a bit from the end that goes into the screw. Partly this is to provide better strength, and partly because of the way the tool is made: if you mash a round bar flat to make a blade, the extra metal is going to flare out. But if you need to get the screw out of the bottom of a hole, you need one that isn’t flared. these are called “cabinet tip”.
Maybe another day I’ll go into detail on the zillions of other screw/screwdriver types (Torx, Robertson, Pozidrive, Mortorq, etc.). For instance there are three or four types that look almost exactly like Philips. Each has advantages and disadvantages over Phillips, and all of them can be worked with a Phillips screwdriver (although their own special driver will work better). And I haven’t touched on mechanical screwdrivers, powered screw drivers, etc.
But that’s the basics of screwdrivers. Go forth and screw things up!