I started using LaTeX for my physics homework because I kept making algebraic mistakes (mostly sign errors) when I'd copy expressions between steps. Ended up saving me time on net.

I use vim now (with syntax highlighting plus some useful macros), but I used nano for a few years and it wasn't too bad either. I compile in the command line and have a pdf open in another window.

I use Kile. Being able to commit, tag and branch in git (heck, just being able to erase a part in the middle and rewrite it without ending up with a chain of arrows across three different pieces of paper) makes things easier to be worth the (slight) writing slowdown, and most of the time I can express myself in latex - after a while it just becomes the language you think in, \int becomes the symbol for integration and so on. Very occasionally I'll write something I know is incorrect notation but close enough that I'll know what I meant, and can go back and correct it later.