Old style slotted screws might be needed if you are restoring or the heads form part of the overall look, but suffer the disadvantage that the screwdriver blade must be exactly perpendicular to the slot to avoid damage. Along came Phillips, which are cross head and sometimes found on factory assembled or far Eastern goods, but Phillips was superseded by posidrive - pz - in most uses many years ago. They are the "new normal" and allow for the driver to be a bit off straight without coming out and make for much faster assembly. As others have said, commonly 3 sizes, pz1 will go up to about 2mm dia screws, pz 3 maybe above 5mm dia but everything in between - most things - are pz2.
Torx is becoming more common, a sort of star shape which you see a lot in mass produced metal things, cars. I bet your car door hinges are held by Torx. They come in a huge variety of sizes, I have drivers from barely visible for cameras and phones up to 40mm for cars etc. They are really good for fast efficient automated assembly and some woodworkers are using them. I got some decking screws last autumn, surprised to find Torx heads, last batch were pz.
If you are starting out, pz probably easiest to get in the sizes you want.
For amateurs the number you use, therefore cost, isn't likely to be a significant part of your total expenses so you can afford to err towards quality. I am a DIY er and converted to Reisser 3 years ago and value the speed, never had one break, and less likely to split when you screw near the end of things.