You need a line with some stretch in it. It needs to be large enough so you can handle it OK. 3/8 is probably as small as you want for easy hand holding. You don't want a high-tech line in this application, as it will have too little stretch. Evans has a short article on line selection on his site
The Right Line for the Job
If you are going to secure the line with a clutch, then you need to also make sure the line size is appropriate for the clutch.
Paul L