You can check the driver that the Printer is using by going to > System Settings > Printers & Scanners. It will look something like this, although I am on OS 15.5, and the circled part shows the driver and the version number should be 3.0 (or possibly 2.0 on an older OS) for an AirPrint install.

Most printer manufactures are now supporting the AirPrint protocol so they do not need to continually update their drivers whenever a new OS version is installed. Before that, when a new OS version was installed, it often broke the driver requiring the printer manufacturer to constantly update them. It really is a win for everyone.
One thing to be aware of for the HP Printers, the last one I installed really wanted you to use their printer refill service, although I was able to opt out. It is fine if you want to use that service, just wanted you to be aware as you would be sent new print cartridges automatically as HP is monitoring your usage over the internet. I purchase my HP print cartridges at Walmart and not sure of the price HP charges for their service, but there is a convenience factor that may be more important to you to have them sent automatically.
For scanning documents, I use the default Image Capture app that is already in your Applications folder. That should automatically recognize your printer. When you first use the app you may be asked to Allow the scanner to use your Local Network, and you must do that.