CTF tools are essential to the completion of tasks, and are extremely diverse, ranging from code debuggers and dissasemblers to image manipulators. Tools allow tedious processes to be done quickly and often make challenges much easier to solve.
The operating system that you choose to use will not hinder your ability to solve CTF challenges, but can affect your speed and access to tools. Each of the three major consumer operating systems have their benefits and downsides, and it is up to you to decide which one you wish to use. Many people decide to either dual boot different operating systems or run them in virtual boxes, giving them maximum flexibility.
Microsoft Windows is still the most prolific operating system in the world, and the majority of all computers come pre-installed with it. The fact that it is based off of MS-DOS and does not run the Unix shell like Linux and OSX limits it's command line abilities, but it makes up for it in large, comprehensive software packages. For example IDA, likely the best dissasembling program, is best used in Windows and is utilized in almost every CTF. Windows is a good option if you are willing to give up simple command line tools and scripts for large, thorough software packages which are often pricey and/or proprietary.
Mac is a very versatile operating system for CTFs, as it can run almost any Linux command-line program while still having nice software packages for general use. It is typically seen as the cleanest and nicest operating system to work with, but at times has limited software options and tools. If you have already shelled out money for a mac, you are well prepared and will be able to run the majority of programs necessary on it.
Linux is typically seen as the 'hacking' operating system, and it is very often used in such context. It has the largest base of open source software and tools, and is based off of the versatile bash command line. If you are comfortable using the command line and want the versatility of quickly writing up scripts and using well-tested tools, Linux is a very good option.
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Linux/Mac - If you want to get started using Linux or Mac and have not had much experience with them, you want to get acquainted with the command line. The majority of these operating system's benefits stem from their command line tools, so once you have a solid basis in Bash you will be able to get started on tasks quickly.
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Windows - As stated before, Windows is based heavily on large software tools, so it would be best to get acquainted with some of its core computer security software like IDA.