Is it on the list of supported AirPrint printers? (See the Apple site for that list). If so, no app should be needed and you should be able to print directly.
Could not get new hp photos shop to work even with my wireless system. App from apple store useless. FYI Canon Pixma 4100 was a breeze to set up and Canon has a free app for iPad and iPhone that works great. You can scan from the printer to the device and send text as well as pictures. HP once was a good co. Had problems with them lately
I use Print n Share which with a minor upgrade can convert any file to a PDF too. This app has worked very well for me with an HP printer. It can print from many apps just make sure it's 'on' before you try to print.
I use the Hp eprint app and it works flawless. I've scanned printed and emailed all on my iPad within the app. Of course you have to have a eprint capable printer, but if you do you can't go wrong with it.
I bought " fingerprint " it has worked great so far wireless and I have it set for 4 different printing settings. Go--- http://www.collobos.com---cost $8.55 w//tax.
DICKSTER-----