Luckily, most Linux distributions include these applications by default, but you also should know the options.
Any GNU/Linux operating system is like a Russian doll. The most central part of it is the kernel. This is Linux itself. Then comes the GNU part of the OS, which is a set of tools on top of the kernel. These tools allow you to make some basic functions. Then, the X-server comes, which is responsible for the graphical part of your desktop. The next layer is a window manager. And finally, facing you directly, is Desktop environment: KDE, GNOME, XFCE, LXDE or something else. Some distributions, though, do not have DE included, but only leave you with a window manager option.
Whatever the external layers of the Russian doll are, there are some cases when you need to dive to the level below the X-server, and run some command directly in the OS. A terminal or terminal emulator is the way to do so.
There are different types of terminal emulators available. X-server, for example, includes X-Terminal. More sophisticated options are Konsole or Yakuake in KDE, GNOME Terminal or Guake in GNOME, and so on. The difference between them, apart from different DEs, is their location on the screen. While Konsole and GNOME terminal are normal windows, Guake and Yakuake are drop-down terminals, which can be minimized into the stripe at the top of the screen.
My personal preference here is just a normal terminal window.
Whatever distribution you use, you may need to edit some text, being it a configuration file, or some personal notes, or maybe some complex document.
There are different types of editors available, from command-line based Vi to GUI tools like LibreOffice or OpenOffice Writer. The other difference here is the functionality of text editors. They can be quite simple like Kate or Gedit, a little bit more advanced like KWord, or a full-scope word processor like LibreOffice Writer.
My personal preferences here are Kate/Gedit for basic text processing, plus LibreOffice Writer for serious documents.
A file manager is a tool to browse your file system and do some actions with it: copy or move files, create directories and so on.
Generally speaking, there are 2 major types of file managers: those that work with single folders at each moment of time and 2-pane managers, although some file managers can switch between those two modes easily.
Most desktop environments have a default file manager. Most often, this is Nautilus in GNOME, Dolphin in KDE or Thunar in XFCE. But the choice is wider. For example, you can use Konqueror as a file manager in KDE too.
Separately, I’d like to mention an old-style classic: the file manager for terminal. Midnight Commander is a leader in here.
I personally don’t have preferences among file managers, and use whatever the default manager in the OS is.
Of course, you can add more tools that you can’t live without in your favourite OS: browsers, instant messengers, multimedia players or graphical editors. They are all important. What are your preferences here?