Linux Ubuntu and WiNEdt under Windows. You can get TeXworks under Windows
as well. All are free except WinEdt, offered only under Windows, which will cost you $20 or $30.
WYSIWYG editors like LyX are great for beginners because they offer point and click features for accessing TeX macros (like \alpha for the letter alpha, \doteq for an equal sign with a dot over it, and so on). Most ordinary (not WYSWYG) editors offer similar point and click features.
I've been using TeX (not LaTeX) for so long that that I know all the macros and I've wrote hundreds of my own macros. This is why I don't use LyX; direct typing, keeping your hands on the keyboard versus switching back and forth between mouse and keyboard is most efficent (in my opinion). In time you become even more efficient, using keyboard shortcuts to TeX or LaTex your source file, instead of point and clicking a menu item.
This should encourage anyone to migrate to an ordinary editor.
The following is less encouraging, especially for those working under Linux.
All the Linux side editors I mentioned previously, Kile, LateXila, gedit, TeXworks, are good but when compared to WinEdt, each lacks one or more signifiicant features. You can google TeX editors and find a huge table comparing them. The issues I have with LinuX editors are subtle and they don't show up in those tables. Kile, for instance, looses its syntax highlight within the definition of a macro, very annoying for long macros. Texworks doesn't let you customize color schemes (though you can goodle this issue and do limited coloring). Some of these Linux editors don't offer inverse and forward search between source file and dvi file.
TeXworks doesn't offer keyboard shortcuts.
I could go on with this list of issues, but the point is that they all come up short compared to WiNEdt. The big problem I have with WiNEdt is its help. I don't know who they thought their target audience would be when they wrote their help files. I think you have to know something about DOS scripting to read WiNEdt help. I sure am not in their target audience. Anyway, a good way to get around this is to google "winedt menu entry" to learn the purpose of a "menu entry" and how to modify it.
This google process will, often times, bring you to this site.
Here's one cool feature of WinEdt. Its syntax highlighting distinguishes system-defined macros from your user-defined macros. The people developing WinEdt really did their homework.
My second choice, the editor I've migrted to when working under Ubuntu, is Texworks. Its free and you can get both Linux and Windows versions.
Anyway, hope this helps. Good luck and try to have fun. Regards -
Jethro