Is it possible to find only apps which are compatible for my iOS version? I have read this question regarding App Store updates for older iPads, and I'm in a similar situation to MrDaniel regarding my hardware / software.

This is a different question though: how to find apps, via App Store or otherwise, which will have a version which is compatible?

In the App Store you can filter by iPhone or iPad, but not by iOS version.

If an app has a compatible version, you can buy it through iTunes on another device, and then on the iPad you can download a compatible version via updates. But how to tell which apps you can do this with?
I've found a great site on that. It shows a list of every app that is compatible with any given iOS version. Don't try to download the app from them, though, just get the name of it and find it on the App Store.