Observation: If you sign out of your apple id, then restart your iPad, you can then open the app store, which loads reasonably quickly. Tap an app you want to download and enter your apple id and everything seems fine.... until you close the app store or switch to a different app.
What's going on is anyone's guess.
That said, I've noticed that on an identical iPad 3 logged into an appleid with only a modest number of apps associated with it has fewer issues. I suspect, that iOS 7 tries to cache your appstore history locally, to reduce server-side activity, make the purchase tab more responsive. The more apps you own, the more data would be cached, resulting in more background downloads, more battery consumption, other data expanding. I also suspect that while this theoretical cache is incomplete the Appstore might well stall. Am I sure about this theory? No. But it would explain some of the appstore issues.
Am I suggesting you abandon your current appleid? No. Does the theory help us? Not really, but it might be worth further investigation.
Another unrelated iOS 7 issue: I've also found that attachments automatically download when I open an email. In iOS 6 I had to tap to download. Yet another annoyiong change. Why isn't there an option to enable/disable automatic attachment downloads?
If someone at Apple is reading this (unlikely) then, please, for the love of all that is holy (or at least Apple's market share), give us back the option to downgrade to 6.1.3, at least until these problems are ironed out.