With regards to the nozzle material, it boils down to two factors: thermal conductivity and wear resistance.
Brass and copper are better at conducting heat, but they have very low wear resistance: use them with abrasive filaments (PLA infused with metal, fiber glass or carbon fiber, as an example) and they won't last a roll. On the other end steel is not a good thermal conductor, and hardened steel is even worse, meaning the filament will get colder within the nozzle, possibly requiring a slower extrusion speed or a higher temperature, but they are quite resistant to wear.
There are other options, like the famous ruby nozzle, which is very wear resistant and, being made mostly of brass, provides a good thermal conductivity, but it's expensive.
Another factor is the shape of the nozzle: some have a very short tip, others a longer one and that also influences the thermal conductivity and the flow rate, but also take into consideration the long ones don't play very nice with very sticky filaments like PETG.
It is a matter of compromise between material, price and versatility, I don't think there is a single best choice.
Usually very cheap nozzles are not machined very accurately, meaning the hole might not be perfectly round or centered, but unless you require a high level of precision they can be considered "good enough": don't get me wrong, I'm not saying those are low importance factors, but you probably won't notice a great difference unless you are using very good filament and printing at high-res.
It will be very difficult for you to damage your printer using a non high quality nozzle, but replacing the nozzle incorrectly (no matter the nozzle quality) can cause damage to the heat block: try not to snap the nozzle thread like I did...
As pointed out in the comments, there are a couple of factors you might have to take into consideration when buying new nozzles: the nozzle body length (there are nozzles with a much longer threaded body, usually referenced as volcano) and nozzles with different thread sizes (M6 for the vast majority, some use M7, very few use a customized system).