Hi Bob! This is a great question, and leads to a very deep rabbit hole. If you have the ability, harvesting greenwood can be a great source of varieties that you can't buy anywhere else (or in appropriate sizes). Storm-fallen trees, trimmed trees, etc... You can use this immediately, but it will likely warp on you as it dries and loses moisture. You can also seal the endgrain to slow drying, for example if you are drying your own spindle stock or you want to turn it later for whatever other reason. You can also purchase pre-dried stock (like you've likely already been doing) if you want to turn immediately with minimal or no warpage. This is all surface-level information. The biggest thing is that the specific project/purpose will dictate what type of wood you need/want, and/or for the wood to become what you need it be (dry, spalted, etc...).
I am certain your question will elicit many responses.