In reply to Voltemands: That would have to be a first generation iPad, not an iPad 2 since iOS 7 is supported on the iPad2. The first generation iPad should be able to run iOS 5.1.1 which I believe is still available through iTunes, and supported.
The problem, as you have spotted, is getting hold of the older versions of the third party apps which are compatible with iOS 5.1.1. This thread on the Apple forums suggests that it is possible, by using iTunes on a computer:
https://discussions.apple.com/thread/5519108?tstart=0
(see the posts by DLR and rbofmd).
As far as I can see the trick is to make sure that iTunes on your computer is set to sync apps with your iOS device(s) and then when you buy an app through iTunes on your computer, it syncs the correct, supported version of the app to your old iOS device. (It would probably be worth checking this method with a free app first, and also checking that a version of the paid app you want was previously available on iOS 5.)
I'm sure there will be other helpful threads on the Apple forums, and possibly even buried somewhere within Apple's own support knowledgebase.