I can give you a quick overview of some of the technologies I have used to build client-side dashboards and applications.
While you can create your own code to manipulate SVG visualizations, I do not recommend it. If you are looking to create customized SVG visualizations, you should probably use D3.js - Data-Driven Documents. D3.js is extremely powerful and flexible and is the underlying technology for many plotting and graphing libraries.
This covers the charting library but does not provide the overall application platform. There are many options to choose from. Keen IO provides a collection of templates that use Bootstrap. Plot.ly also provides a provides a solution for creating interactive dashboards. If you need something more complicated, you can always use a web application framework like Angular, Polymer, or React.