Free LaTeX editors are available for almost every platform. Be it Windows, Mac or Linux, you will find a large choice of great tools and editors. The editors are - with some restrictions - compatible with other editors and operating systems. Thus it's a great choice for collaborative papers as well.
List of $\LaTeX$ Editors and Bundles
These are some popular choices to create LaTeX documents:
- MiKTeX (Bundle) (Windows)
- Texniccenter (Editor) (Windows)
- Mactex (Bundle) (Mac)
- Texlive (Bundle) (Linux)
- Lyx (Bundle & Editor) (Windows, Mac, Linux)
- Texmaker (Windows, Mac, Linux)
- Overleaf (Collaborative Online Editor)
How to choose an editor for $\LaTeX$
I personally use emacs and texlive on a Linux machine to create my documents. Using a text editor instead of a dedicated editor works best for me and this way I make sure that my files compile on various platforms. This is important for me, since I create a lot of collaborative works and I experienced a lot of trouble in the past when one guy on my team used Lyx to create his documents.
While Lyx is certainly a great choice if you're a beginner, especially due to great features like the formula editor which makes creating documents as simple as pie, it creates LaTeX code which is hard to read by humans and doesn't work well when embedded in collaborative works. I recommend using either a text editor or a dedicated LaTeX editor along with a bundle, which let you see the actual code and manipulate every aspect of your document.
Another alternative which came up recently, is the collaborative online editor from Overleaf, which is similar to google docs, but much more powerful, since it's backed by LaTeX and integrated with Dropbox and other cloud storage services. Since most (or all) or the editors are free, you can just try a bunch and stick with the one you like most. I don't think there is a particularly bad editor around, it's just a matter of personal preference.