Since others touched on the Morse taper and other items….
Chuck: Most take an insert but some are direct threaded. The insert allows you to use it on different lathes (or if you upgrade to a different size at some time). The direct threaded matches you spindle size (such as 1X8tpi or 1-1/4Xtip). Better quality chucks have a wide range of inserts available.
For the drill chuck (Jacobs chuck) it is attached to a taper and is inserted in the tailstock. It is a chuck but not in sense of a lathe chuck (4 jaw scroll chuck) which mounts on the threaded spindle, it is simply like the chuck on your hand drill.
I think decent quality HSS steel is the tools you need. There are tools with carbide tips but they are more specialty tools and will not do all that you will need them to do. If you let us know what type turning you are looking at doing (spindle, bowl, or both) you may get a more definitive answer as to suggestions.
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