My printers work quite well. I have a CUPS server with avahi/nss-mdns. Nothing special is needed on the phone with this, printing "just works". I couldn't tell you much about hp printer applications, I wouldn't trust it. I don't even trust my two HP printers to access the internet because they like to take firmware updates to block the usage of 3rd party cartridges, so I have my firewall set up to block their access while allowing them to remain accessible on the local network for printing.