I have a set of ER 25 collets hindsight I should have got a set of ER40, ofcourse the size of your lathe will depend on what size you buy.
The Morse taper collet chucks are cheap,it cost me about $30-$40 for the pair of 2MT and 3MT
I use them for when I make bullet pens etc, they grip all the way around the item evenly and don't mark the project.
Try a turning 3mm dia item in a drill chuck.