How can I use google app engine?
It is hard to say if App Engine is suited to your particular needs without more details about what functionality you want your web store to present.  It also depends a little bit on your background and experience.
However, the "app like feel" and crafting a "completely unique feel" for your site is something you can accomplish on any reasonable platform - I expect the presentation style will be relatively independent of the backend you choose.
I've begun planning a kind of web store interface that I want to work on soon. I'm starting to import products from China and want to have a completely unique feel for my site. Now I'm kinda a google fanboy and have heard alot about google app engine. Mostly I like the hosting available with google more then anything though. But I wanted to know, would the App Engine be good for what I'm making?
Namely a web store with an app like feel. I've decided, to help if I ever need to move my host, to work in web2py hosted in the App Engine. Or would I be better with django or something on a normal host? 
Is google best for webapps? Or is it pretty well suited for webstores as well?
Thanks