Any inkjet printer is going to have the ink clogging problem that you describe. The printers are designed to perform certain priming functions periodically to clear the nozzles, but if you are using it only once every six months, then you are likely to have problems. The newer inkjet printers are going to make this problem even more costly. In older model inkjet printers, the ink cartridges were sold with an integrated printhead (the silicon chip with the nozzles), but this made cartridges very, very expensive because each ink cartridge had to be equipped with its own silicon chip. Most of the newer inkjet printers are sold with a single, permanent or semi-permanent printhead that is shared by all the ink supplies. The new ink supplies are often referred to as ink tanks (as opposed to ink cartridges) because the tank is now just a plastic box of ink that feeds into the permanent printhead installed in the printer. The upside to this design is that ink tanks are cheaper to make (and therefore cheaper to purchase) than the old ink cartridges because the ink tanks do not require individual printheads. The downside, from your point of view, is that if the printhead gets clogged, its time to replace the entire printer or at least the most expensive part of the printer -- the printhead.
Laser printers have a different set of pros and cons but clogged printheads is not an issue given that they use toner supplies rather than pigmented, aqueous ink. The downside with laser printers are that they tend to be more expensive (both in terms of the initial hardware purchase and the cost of supplies) and they do not produce photo-quality prints. There are a number of online websites that you can use to purchase prints of digital images, so that would satisfy your photo-quality requirement, but there is not an easy answer to your requirement of a printer that you will use only a couple of times a year. A laser, especially a color laser seems excessively expensive for such low usage, and an inkjet printer is likely going to have issues with clogged nozzles.