I concur with you that IntelliJ is great, JetBrains consistently produce superb tools. I use the WebStorm for all my front-end coding (mainly for JS code completion, linting and refactoring), and ReSharper for serious productivity and refactoring when i'm doing back-end stuff in Visual Studio. ReSharper is possibly the greatest IDE enhancement of all time.
Funny you mention jEdit, it was my text editor of choice when i was at university - we were encouraged not to use tools that hold your hand like Eclipse or NetBeans. My only fear is that if i try to build something big in jEdit (i'm thinking thousands of lines of code) it'll become a maintenance nightmare working with nothing but text files - i think i'll eventually need something that has a concept of projects etc. or am i missing something here?
I'm starting to gravitate towards Python and Ruby as primary choices of language as they're both popular and seem to have well-established web frameworks.
If you go with Java or Scala, Eclipse, IntelliJ or NetBeans are good choices. Personally I prefer IntelliJ where you can check out the community edition.
For scripting languages such as php, ruby or python, vim and emacs are the goto editors (i use emacs myself). On the other hand IntelliJ and Eclipse have plugins or alternate builds for these languages as well.
If you come from .NET and your main goal is to broaden your horizon, I'd definitely try to go with a plain text editor like jEdit or SciTE and pick a scripting language.
Since you said you're into webdev, the rails or django frameworks will probably get you the most bang for your buck.