I have this problem on my iPad 3 (A1430) too. I experiencd no problems with the AppStore prior to iOS7.0 / 7.0.2. I've done a great deal of experimenting with settings, resets, restores, recovery mode etc. Nothing seems to fix it, although there are some things you can do to temporarily work around the problem.
Things to try
Important: Backup your iPad via your computer's iTunes or to the iCloud (see http://support.apple.com/kb/HT1766 ).
Check that the AppStore credit card security code prompt isn't causing a problem
The payment verification panel used to pop up after restores, so it's odd that it never seems to pop up now. Open Settings > iTunes & App Store > tap your Apple ID name (it should be blue) > View Apple ID > enter password > Payment Information. Enter your credit cards security code in the "Required" field. Tap Done. Open the AppStore and try again.
Re-sign in to the AppStore
Open Settings > iTunes & App Store > tap your Apple ID name (it should be blue) > Sign Out.
You should now see space to enter your apple id. Leave them blank. Restart your iPad by holding the Sleep/Wake and Home buttons down simultaneously until you see the apple logo appear and then lot go of the buttons. Once your iPad has restarted, unlock it. You should be logged out. That is, Settings > iTunes & App Store should still be asking for your apple id. Do not enter your apple id details yet, even if prompted. Now, open the App Store app. It should open quicker than before. You should also find it fairly responsive to searches.
Weirdly, if you search for apps you already own, they will appear with the download from cloud icons as if you are logged into your apple id, even though you aren't.
At this point, search for an app you want to purchase (paid or free, it doesn't matter). You will now be prompted for your apple id. Enter your details and the app should download normally.However, this didn't fix the problem for long. It returns for me either with the next purchase or sometime soon after.
- Reset All Settings
Note: This resets most of the iPads settings back to factory default, including your WiFi connection setup.
This didn't really help much on my iPad, but it's probably worth a go.
In Settings > General > Reset tap Reset All Settings. Confirm and wait for your iPad to start up again. Enter your WiFi settings and try the AppStore. Search for the app you wanted to purchase and tap on the buy/download button. You will be prompted for your apple id. Enter it and the app should start to download.
- Restore iPad
IMPORTANT: You really do need your iPad backed up before you do this!!!
Either:
a) Perform a restore via iTunes: Before restoring can take place you must deactivate Find My iPad (Settings > iCloud > Find My iPad: Off ). Then follow the instructions at http://support.apple.com/kb/HT1414 .
b) Skip deactivating Find My iPad by forcing your iPad into Recovery Mode (see http://support.apple.com/kb/HT1808 ). This route will require you to login to your apple id to authenticate ownership of the iPad before it can be used. Either way, you will have the option to restore your backup or set up as new. I recommend using Set Up As New for testing purposes, then use iTunes to Restore your backup if the AppStore works well for you over a few days. For me, Restoring the iPad works best, but it's not a permanent solution. The AppStore will get slower and slower over time, eventually returning to it's slow, buggy, unresponsive, crashy ways.
Possible, but untested workaround
Assuming the problem is caused by as described below (see Possible cause section), it might be possible to fix the problem by hiding all of the apps you don't wish to ever use again (disappointing freebies at a guess). You can do this using iTunes (PC/Mac). Open the iTunes Store. On the right of the Home/Featured page theres lots of links. Click on the Purchased one. Next click on the Apps tab (top middle-ish), and then iPad (top middle). After a while you should see your apps listed. Move the mouse pointer over an apps icon and you'll see an x in the top left corner of the icon. Click the x and the App is hidden. You can unhide them by viewing your Accounts page (click you email address, login and scroll down to Hidden Purchases).
Possible cause
(Experience-based speculation)
There are some good indications that the AppStore is caching purchase data in iOS7 - something that didn't appear to happen in iOS6 or earlier. The more purchases (paid or free) on an apple id, the bigger the local cache on your iPad/iPhones/iPod SSD becomes. While the cache is building, and while its still small enough to load into RAM, the AppStore works fine. However, when the cache grows too large to fit in RAM, I suspect the AppStore attempts to page results from the SSD, crippling performance and destabilising the app. The threshold of how many apps it takes to cause the cache to get too big probably varies depending on iOS device model (the more physical RAM, the larger the cache it can accommodate). However, I suspect you need to have a significant number of apps (1000s) before you run into problems.
Why I think there's app purchase caching in iOS7 :-
If I open the AppStore after a restore (as new), sign in to my apple id and wait for my purchases to show up with the "download from cloud" icon in search results, then logout of my apple id, restart my iPad, open the AppStore without logging back... (breathe!) ...I can still see the "download from cloud" icon on my purchases. The icons turn to prices if I attempt to download one, and cancel the apple id login.
It's also noticeable that "other data" (in iTunes (PC/Mac) iPad > Apps) grows with every sync at a steady rate (about 0.1Mb every 2 minutes) from the moment the an apple id is logged into. Likewise, the iPads own Total Usage figure (Settings > General > Usage) grows continually even when there is no activity on an iPad freshly set up as new, with no app downloads, in standby. So something in iOS7 is filling the SSD - also consistent with caching, although there are other plausible explanations for this.
And then there's the performance of the Purchased tab in the AppStore (shortly after a restore, while it's still working). Results appear much faster than in iOS6. Far faster than say searching for a fairly uniquely names app. Ping defyingly fast. Again, points to locally cached data.
Ideally, there should be an option to disable caching entirely or an automatic fallback-to-server mode when the device can't cope with the cache. Personally, I'd rather the AppStore worked a little slower, but worked for everyone. As it is it works quickly for some, and hardly at all for others. I'm not particularly thrilled about the additional SSD usage either.
Bring back the iOS5 AppStore (more efficient that the iOS6 one re paginated Purchased tab, and actually worked unlike the iOS7 one).
Ideally Apple would let us roll back to 6.1.3 until these problems are worked out, particularly on the iPad (which has considerably more iOS7 bugs than the iPhone). As it is, let's hope the problems with the iOS 7 AppStore is fixed sooner rather than later.