The current HP problem is probably temporary - but a pain in neck right now. And if the printer is 10yo, it probably deserves an update.
Normally for reliability, and consumable costs, I'd recommend HP - Hey Ho!
Having said that - I currently have an Epson - which I bought because it has high capacity ink tanks filled (painlessly) from a bottle - so the running costs are low and I can print photos again without worry (having said that, the printer itself costs a lot). This Epson works perfectly wireless, so I guess other Epson wireless models would too.
The one I have is a dedicated photo printer, the ET700, which has an additional "photo black" ink tank. This is close to the most expensive inject Epson do. I don't know where you are, so I'll not give a price but you can look it up.
If you don't need ultimate photo quality, then the more conventional ET2710 is more reasonable, and will still do good photographs. These "eco tank" models might be more expensive than an ordinary cartridge inkjet, but you'll find once you've used the included ink, you'll have spent less than the ordinary printer + cartridges for the same amount of printing. And will save significantly in running costs from then on.
The main benefit of these for me - is I no longer concern myself with ink costs which means I use the printer far more, and actually get value from it.
