There is no such thing as a home screen in an iPad browser. Looks like you have an active link that is directing your browsers to the App Store.
Swipe up the screen, or double click on the home button. Your current app should minimize to the centre of the screen. Then swipe up to close apps (make sure you get your browsers in this fashion). Nect time you start your browsers, the offending behaviour should be gone.
Wouldn't hurt to do a reboot at the same time. Press home and power buttons together until the Apple logo appears, then release both buttons. Wait for the iPad to restart and all should be good.