Can you describe the paradigm shift that is necessary?
Imperative vs Declarative
With jQuery you tell the DOM what needs to happen, step by step. With AngularJS you describe what results you want but not how to do it. More on this here. Also, check out Mark Rajcok's answer.
How do I architect and design client-side web apps differently?
AngularJS is an entire client-side framework that uses the MVC pattern (check out their graphical representation). It greatly focuses on separation of concerns.
What is the biggest difference? What should I stop doing/using; what should I start doing/using instead?
jQuery is a library
AngularJS is a beautiful client-side framework, highly testable, that combines tons of cool stuff such as MVC, dependency injection, data binding and much more.
It focuses on separation of concerns and testing (unit testing and end-to-end testing), which facilitates test-driven development.
The best way to start is going through their awesome tutorial. You can go through the steps in a couple of hours; however, in case you want to master the concepts behind the scenes, they include a myriad of reference for further reading.
Are there any server-side considerations/restrictions?
You may use it on existing applications where you are already using pure jQuery. However, if you want to fully take advantage of the AngularJS features you may consider coding the server side using a RESTful approach.
Doing so will allow you to leverage their resource factory, which creates an abstraction of your server side RESTful API and makes server-side calls (get, save, delete, etc.) incredibly easy.