In anteCovid times the absolute best place to start is a quality class.
You could go to John C Campbell or to David Ellsworth’s for a long weekend or connect with a mentor/teacher from a local Chapter.
In the classes you not only learn basic skills that make turning rewarding an pleasurable but you also get an appreciation for what features to look for in tools.
my suggestion for getting started is to spend the first few months on spindles,
Learn beads and coves, then re learn beads and coves, then practice beads and coves.
All forms in turning are made from combinations of beads, coves, and flats.
for tools - 1/2” bowl gouge, 3/8 spindle gouge, parting tool.
For a lathe get a used mini or midi - 10” or 12” swing. Most turners with big lathes have one of these.
Get a grinder set up with a sharpening jig system (woulverine ).
For a Chuck get a vicmarc 100 or Oneway talon
after 3-4 months of spindles on the small lathe you will want to move up to a larger lathe like a jet1840
turn five each below and you will be an accomplished turner
carving mallets, gavels, goblets, set of 4 napkin rings, spheres, mortise& pestle, boxes, hollow ball Christmas ornaments,
For extra credit-
Pens, bottle stoppers, pepper mills, salt mills