If you are buying a new printer
There are lots of threads here about not being able to print. So I thought I'd do a quick post about the opposite, being able!
I bought an HP Photosmart B110 Series. It was not in the Apple list at the time, but was clearly marked on the box "Compatible with iPad".
I can print to it two ways. One is wirelessly, when I go to Print and Share for example, I select the choose printer option, and if the wireless printer is switched on, it finds it straightaway, and prints.
But, there is another way (and now my mother knows about it, a flipping annoying way!)... she can email straight to the printer. When I took it out of the box and set it up on it's little screen I went through the options and assigned it an @hpeprint.com email address. This means whether I am sitting next to the printer, or 12,000 miles away, I can still print in seconds. It takes no setting up in the iPad at all, and best of all, the document prints with no email headers or footers... whatever your document is, is what gets printed.
Anyway, I thought I'd mention this, in case people were still having some trouble. The printer is a good printer with card readers, USB ports for Windows etc... and was the great price of £39.99, so nowhere near as expensive as Apple's recommendations.