Personally, I'd be very wary of any printer that requires you to install an app in order for it to work with your iPhone. In this day and age, you just want to be able to send something to your printer from the app that you're using at the time, without any further complication.
If you buy a modern printer and it says 'Airprint' on the box, it should work automatically without any further software.
I got an Epson XP-402 recently, and it was a breeze to setup. Just used its front panel to find and connect to my WiFi router. Then it was visible from any of my Apple devices, and any app that supports printing can print to it.