Search the forum for "chuck" or "scroll chuck".
For your purposes, the first chuck a woodturner would buy would be a scroll chuck (see the wikipedia article here,
https://en.wikipedia.org/wiki/Chuck_(engineering) ), but understand that woodturners use 4-jaw self-centering chucks (for the most part). A "standard" chuck will typically come with 1 set of jaws and 1 worm screw.
Generalizing: The quality (smoothness of operation, precision, durability, etc.) of chucks and their pricing tends to be correlated. More expensive chucks tend to have higher quality than less expensive chucks--but a less expensive chuck may be perfectly adequate to your needs. Once you buy a particular brand of chuck, additional jaws/accessories tend to require statying within that brand family or model. Some exceptions: Nova jaws are generally interchangeable with Record Power; Nova jaws are compatible across Nova models; Axminster jaws are compatible across Axminster models.
Opinions:
- Least expensive: "Barracuda" (house brand), from Penn State Industries
- Nearly as inexpensive: "Apprentice" brand, from Craft Supplies USA (woodturnerscatalog)
- A bit more expensive, no personal experience (hereafter abbreviated NPE): Grizzly
- Mid-line: Record power (NPE), Teknatool (Nova), Oneway (I like the smoothness and precision of the Oneways a bit more than the Novas; I also dislike the Nova "direction of tightening"), Hurricane (NPE), Chucks Plus (NPE)
- A bit more expensive: Axminster
- Most expensive: Vicmarc, Easywood tools
p.s. Edit added: BTW, welcome!