Depending on your distribution, the packages for LaTeX will be different. The following list describes how to install LaTeX on some of the more common distributions:

Ubuntu

Run (as root) apt install texlive-full. This will install most of the things available on CTAN for you.

Fedora

Run (as root) dnf install texlive-scheme-full.

Arch

Run (as root) pacman -S texlive-most biber

NixOS

Add pkgs.texlive.combined.scheme-full to environment.systemPackages in your /etc/nixos/configuration.nix.

For editors, I recommend the following:

Emacs + AucTeX

High-power, and very configurable. I'll talk about it in a later video.

Gedit

A programmer's text editor from the GNOME project with LaTeX plugin.

Kate

The KDE Programmer's Text Editor

Install the MiKTeX distribution following these instructions. It includes an editor called TeXworks, but you may also want to look into something like Notepad++.

Edit: You may also want to look at TeXnicCenter which includes a comprehensive editor and an installer for MikTeX.

Install MacTeX from the TeX Users Group, it's a complete TeXLive distribution, and can be customizable. Use these instructions. This comes with the TeXShop editor, but I hear good things about Sublime.

All of the platforms above support my recommended editor, Emacs & AucTeX. Using it on Windows requires a bit of configuration, but it's worth it.