If you want to use Extjs only with asp.net classic I recommend to use http://www.ext.net .
I started use Ext.js with asp.net and faced a lot of problem, then I discovered them and start use it from version 0.4 (now it's 2.0).
If you don't want, the suggestion is to interface client pages with ashx handlers and invoke them via store.sync().
Another solution (I tried years ago) is to manually create asp.net post via __doPostBack(eventTarget, eventArgument) asp.net client function within your store events for each CRUD method.
Stefano