IMHO there is none. Doing even decent, not even speaking of good, photo printing requires a very expensive inkjet printer.
I used to have a not so cheap inkjet. I eventually ditched it, bought a color laser printer for documents, and use self-service print machines or online print services. This costs less than using an inkjet, given the price of ink cartridges. The current prices on good machines:
- 0.35€ for 10 x 15cm (4"*6")
- 0.70€ for 13 x 18cm
- 2.50€ for 20 x 30cm
(and decreasing prices for volume printing).
If you don't print often, you end up spending a good chunk of your precious ink cleaning up the print heads (which is mostly done by blasting ink through the print jets).
Avoid HP like the plague and especially their ink subscription scheme.
I'm very happy with my Brother laser printer, because it works with standard drivers (so works very nicely with Linux) and you don't need all these proprietary applications.