There are multiple options. R8 is a tool holding collet, so not very good for holding anything that could be longer than an end mill shank, and you can’t add a depth stop to repeatedly machine multiple parts at a time. 5C or ER40 is much better on the lathe.
Depending on what you want to do, ie how many like pieces at a time and how quickly you need to get them done, you can go with something that is more production oriented like Royal lever collet closer, or a Sjogren type speed chuck, or you can go more economical with what David posted above. I have both the 5c and ER40 chucks David posted, but in D1-4. They are not bad for the money, but both needed some fine tuning. I started with the ER40 chuck and quickly added the 5C due to its limitations with machining short pieces.
If I had the money for a Bison 5c collet chuck, I probably would have spent a bit more and gotten the Sjogren chuck. I couldn’t use a lever collet closer on my lathe since the saddle does not come close enough to the spindle to use an adapter in the spindle, I would have needed to collet nose about the same length as the collet chucks, so decided against that choice. If you like the lever style, see how close you can get your tool to the spindle to see if a simple MT whatever your spindle is to 5c adapter would work, or you would need something that sticks out further.
I like my ER40 collets a lot, but they don’t work well with short items for second operations, so you might need to eventually get a 5C system anyways.
This company has a variety of the products I mentioned to give you an idea of the differences.
Rovi Products is a leading supplier of CNC & Manual Collet Chucks. Styles include: True Length, Pull Back, Quick Grip, Air, Manual, & Wrench Operated.
www.roviproducts.com