Integrating external web application
About What is the best way of using Drupal as a front end to an existing web application?: I leave it to others to decide if it would be the "best" way, but "a" way to do so is to continue to use your existing web application for maintaining the data of it, and then use Drupal as a frontend to actually visualize those data (read only operations).

Assume the DBMS involved is some type of PDO compliant DBMS, e.g. MySql (the question currently does not provide details on that). So similar to what is described in Python Web Application Development Using Flask and MySQL. In that case the Forena module would be a perfect fit to get the job done, i.e. build reports and/or charts about data stored in your existing web application. Here is a quote about Forena:


  ... built of the idea of using SQL to get data out of a database and use XHTML and CSS to format it into web reports.


Possible DBMSs that could fit this approach are the Drupal DB itself (of course), but also MySQL, Oracle, MS SQL, Postgress, Sqite, anything PDO compliant.

The advantage of this approach is that you get lots of Drupal features avilable, while the "bacckend-part" of your application continues to be the applicationn you already have (you don't loose the investements made in that).