There are actually thousands of different operating systems for personal computers, but in terms of common use, there are three main categories: Microsoft Windows, Apple iOS, and Linux, each having their advantages and disadvantages.
For compatibility, Windows is probably the best operating system, since so many people use it around the world. Windows is a popular system among businesses and there is a lot of software written for Windows machines. Also, Windows runs on many different brands of hardware, so the user has a lot of choice in this area. Microsoft is prompt about updating the system. Finally, because of the popularity, many open source software programs are available for a donation to Windows users.
One problem with this kind of popularity is that people who write computer viruses are more likely to write them for Windows systems than for other systems. Another disadvantage to Windows is that the operating system tends to take a lot of resources on the machines, leaving less room in RAM and also on disk for programs. Finally, some computer users dislike what they feel is paternalism on Microsoft's part, especially when system updates prevent a user from shutting down the machine at will.
Apple creates both the operating system and the hardware on which the software is installed; it had a brief encounter with the Microsoft model (one operating system for many different computer brands) about twenty years ago, and that didn't work out for them, financially speaking.
Many people who use iOS computers and other Apple products such as the iPhone, absolutely would not use any other system. Apple inspires brand loyalty because of the aesthetics of the machines and the software associated with them. iOS machines are particularly popular among artists of various sorts as well as educators because of the high quality software available.
A main disadvantage of Apple products is the expense. The hardware costs a lot more for less computing power than a Windows machine. Software tends to be proprietary and expensive. A second disadvantage is compatibility; while some programs run on both Windows and iOS, others are not available for iOS. Some iOS programs yield files that cannot be opened by non-iOS programs.
Linux is a huge category of operating systems, as there are thousands of versions of Linux available to address many different types of users. Linux distributions ("distros" or operating systems) are generally open source, sometimes with corporate support, which means that many programmers volunteer their time to develop and maintain the various distros.
Advantages of Linux include that these operating systems often take fewer resources, so a Windows machine that runs slowly with a full disk drive might run much faster and have a significant amount of room using a Linux distro. Also, there are, for some popular distros, 50-60,000 open source programs available. Admittedly, some of these programs might not be great, but others are professional quality. Linux also allows for maximum control by the user through the terminal, which is easily accessible. Finally, even if you have an old machine without many resources, there may be a lightweight distro that will run on it and make it usable.
Linux tends to be a little more challenging to install and use, although ease of use has increased phenomenally over the last twenty years. Ubuntu, one of the most popular distros, has become relatively easy to install and use and there are others that are fast upon its heels. There are some programs that are not available for Linux, so compatibility issues may occur, and serious gamers find Linux frustrating for this reason.
Technology is changing incredibly fast. Because of the popularity of tablets, since they are lightweight and their functions continue to increase, Android may also become a more prominent operating system for people's primary computing needs as laptops begin to fade into the background. It is likely that Linux distros will begin to run on tablets; Microsoft and Apple are already working in this area.