I had a similar gig a while back, perhaps even the same one. Maintaining a mammoth Classic ASP site with spaghetti, no worse, server side code and 1000's of pages, much of which was duplicated except for a word here or there. Nested includes, also duplicated, hardcoded connection strings all over the place, arghh. Finally had to tell the client I needed to move on, but I digress. VS works fine for debugging server side code. You have to set up IIS on your dev box to run the site locally, set IIS for local server debugging, run the site then from VS use Attach to Process to establish the connection to IIS. VS will break for you then. For client side debugging you can make use of IE's debugger (F12) or any of the other such as Firefox or Google's, they will step through client side javascript, oh wait, your site probably doesn't use javascript, not yet anyway (see below) :-). Once you get the debugging thing worked out you can slowly introduce more modern concepts such as javascript and ajax and even jump in and out of .NET for certain pages (I used MVC 3 cause the routing needs to be set properly, might be do-able for other view engines I dunno).
Steve the Coffee Guy