Is there anyway to access web version of app store?
You can actually access the app store through a web URL.

It is referred to as iTunes Preview.
It is mostly text links until you land on the product page.

The web addresses are as follows.

All Itunes Selections and Cetegories: https://itunes.apple.com/us/genre/

Just Apps (AppStore): https://itunes.apple.com/us/genre/ios/id36?mt=8