First let me say that it can be addictive.....and somewhat costly. The slope can be steep. Before spending lots of $$ maybe you could find someone in your area that has a lathe that would do a little mentoring and let you use their lathe to see it the bug has really bit you. Woodcraft in Raleigh has classes that are not expensive.
If you are ready to boost the economy, sometimes there are good deals here in the classified, also check
craigslist.
You will need a lathe, some lathe tools (Harbor Freight has two fairly good starter sets that are between $35-50), a method to sharpen the tools, mandrels if you are doing pens, live centers, dead centers, chucks, etc., etc., etc.:tool::tool::tool:
Delta, Jet and Rikon have midi/mini lathes, Harbor Freight has two (I understand only one is worth the noney) and there are a few others that are good starter lathes. I have had a Delta Midi for almost two years and it has done all I need to do as I continue to learn. I have turned lots of pens, some bowls, lidded boxes, spindle work, tool handles, etc. But the urge to upgrade is creeping in but the $$ are not available yet.
If you were closer you could come try mine out.
Try to get on the list for the
Good Will Lathe owned by this forum.
Good luck.