Q: Cant set up my HP office jet 8600 printer with my iPad mini

That is not an AirPrint supported printer. Check for compatibility here: http://support.apple.com/kb/HT4356

Check the App Store for an HP app that may provide limited printing functionality. Alternatively, you can use your computer as a wireless print server using an app like Printopia. Note that your computer must be on and able to print for this solution to work.