What are the best LaTeX editor/compiler?

Texmaker is a very good cross-platform LaTeX editor. Installation link: Texmaker

Didn't quite understand what you meant by 'editor/compiler that does not show the output until it is done'. However, I'd suggest Kile. It is the only one which gave me output despite any unmet library dependency. I've tried a few others without success, even on Windows 7 (although some seem to work excellently on Windows XP).

Install kile with the command in a terminal:

sudo apt-get install kile

What I like about gedit with the gedit-latex-plugin is that you can configure your own snippets with shortcuts. For example, if you use \mbox{text} often, you generate a snippet \mbox{$} with the shortcut tab-mb, so you just have to type tab-mb to have the mbox latex command with the cursor positioned in the place where you placed the $ in the snippet.

To install it:

sudo apt-get install gedit gedit-latex-plugin