I plan on developing mostly browser-based applications. I'll go to lower-level non-scripting languages when I need server-based utilities.
Javascript is really taking off on the server-side, as node.js. node.js is the cutting edge for server-side web apps, they're about to release version 1.0 which will have windows support (as in, you'll be able to host your node.js webserver on Microsoft Windows).
JQuery is the best place to start. For fancy stuff, look to css3/html5. If you want to get really fancy, check out d3.js - it uses a jQuery-like syntax.
Just keep nibbling at it, playing with demos and example code. Think of something you want to make and just try to build it.
When your code starts getting to 100+ lines (the javascript code, not including the HTML markup), you should start thinking about code structure. Ruby on Rails got famous because it was great at providing an MVC framework for web apps. Coding anything beyond the most simple of web apps can get really hairy when you just start pasting together PHP scripts.
That's why people use frameworks. jQuery is great, but its not a framework. If you're doing a client-side app, unstructured jQuery can get very hairy beyond 100 lines or so. Changes get harder and harder to make and the complexity gets unmanageable, and bugs get more and more common because of all the unintended side-effects when different parts of your code are all using global variables. As an intermediate with javascript/jquery, I have been learning this the hard way very recently.
Writing structured, maintainable, modular code becomes very important. Using objects, and choosing the right 'design pattern' for the job is how you do this. MVC is basically a combination of several other more basic design patterns. Essential JavaScript Design Patterns For Beginners is a great online-book for getting familiar with design patterns. It just got a substantial update the other day. There's a chapter on how to use design patterns with jQuery.
backbone.js is the most popular MVC framework for javascript. It can run on node.js for the server-side, as well as used on the client-side (code can even be shared between the two, simplifying the development of a web-app). It is fully compatible with jQuery.
Remember, jQuery makes it easy to lots of things, but it doesn't provide a framework for structuring an app - which will be the challenge you face after getting past the basics.
Don't worry much about MVC and design patterns for now (you will later if your app gets complex enough). Take a look at the source code for bitcoinmonitor.com - its completely unobfuscated: http://bitcoinmonitor.com/static/heartbeat.js. He doesn't use any fancy design patterns, but his code is well-structured. But if you read the code in the libraries he uses (flot code), fancier design patterns are used.
