Safety First
The first tool that a new turner should buy is a full-face shield.
Starter Set of Tools for Spindle Turning
My suggestion is this five-tool starter set for spindle turning:
(a) Spindle roughing gouge – 1 ¼" wide (32 mm)
(b) Spindle gouge – ½" shaft size (13 mm)
(c) Diamond-shaped parting tool – ¾" (19 mm) wide by 3/16" (5 mm) thick at the tip.
(d) Narrow parting tool – 1 ¼" (32 mm) wide by 1/16" (2 mm) thick
(e) Skew – ¾" (19 mm) wide by ¼" (6 mm) thick