Go for a range of devices perhaps. Get a cheap china phone, get a HTC and a Samsung and that covers the widest variety of manufacturer OS I guess.
It's well worth noting that a Nexus device (e.g Nexus 4) will let you test the latest version of android (currently 4.3) at a reasonable price. You'll get updates fast so you'll be able to test the functionality straight away.
Also remember there is an emulator in the SDK that will help you see how it will look on different screen sizes, dpi, hardware etc.
From my limited experience HTC are the trickiest due to Sense getting its roots into everything.
There's no real perfect answer to this question. I don't see a need to buy 10 devices, but a few different brands and the emulator should keep you going initially. Also don't forget there's the community out there that will install your app and give you feedback. You could use XDA for this, or just feedback on the Play store. Give an incentive to the user to report on bugs / issues etc and they'll take care of a lot of that. As you know people are fast to tell you your app has issues!