I will second Elwin's suggestion. Get a collet chuck for ER32 collets. You will find endless uses for it. There are two "versions" of the chuck. One threads on the nose spindle threads, the other has a Morse Taper on it. The only difference is that with the Threaded flavor, you can stick the stock through the head stock, but on the MT one it is solid and you can only put about 2-3" into the collet. Use a drawbar for the Morse Taper version.
The clamping range for a collet is about 1/16" or 1mm. Try to get the Metric collets. An 18 piece set will clamp on the entire range of size from about 1/8" to 3/4" without "gaps". With the Fractional set, there will be small sizes above 1/2" that you can't clamp down on. YMMV
I bought a collet chuck and a set of collets a few years back, and have found that they are very useful. If you can make a tenon, a collet chuck becomes a secure way to mount it.
As Randy said, the screw-on variety is more flexible because you can mount long items that are thin enough to fit inside the headstock spindle bore. While there are some orphan brands out there, the main options for screw-mounted chucks are Beale, PSI and CSUSA. The PSI and CSUSA sets come with a chuck, a set of imperial-dimensioned collets, a thread adapter to fit a different spindle threading, and tommy bars. Beale sells both individual collets, and collets in sets, and offers a range of native spindle threadings.
I bought the PSI set, and have been pleased with it. However, the collets came in 1/8" increments, and as Randy noted, that means that there are gaps in the range of diameters that those collets won't grip. While that's not totally convenient, so far I've been able to live with it.
You can buy sets of Chinese-made metric collets that range from 2-20mm with no gaps from Amazon, but that's an added cost. In hindsight, I think the least costly approach to acquiring a full-range set would be to buy the collet chuck (alone) from Beale, and then buy a metric collet set from Amazon.