Do I have to bury PVC pipe if used outdoors?
PVC does not need to be buried, however the advantages are:


Protection from impact breakage (schedule 40 PVC is relatively brittle and can break easily).
Protection from UV light (PVC like most plastics is affected by UV, this can be overcome by painting the pipe).
Protection from freezing, if buried below the frost line.


As for pipe size, it depends on the size of hose spigot you use. It will most likely be 1/2" or 3/4" (some come with both sizes). When dealing with different materials, use the same nominal pipe size (3/4" copper = 3/4" PVC).

Personally, I would look at using PEX pipe and bury where possible. The exposed pipe will be less susceptible to breakage than PVC. Also due to its flexibility, you can run it without the need for additional fittings. If you don't have PEX crimpers, you can use Sharkbite push-on fittings (the same fittings can be used to transition from copper to PEX).