Quite often on my travels I end up teaching random passers by to sling. However, I'm never quite sure what technique to teach them first.
I usually start with underarm but it does strike me as quite a dangerous one with rocks often shooting straight up or behind in the hands of a beginner. After a time most people pick it up- I always stress to do the initial rotations slowly to make it easier to time but still...
I've also had some success teaching a basic overarm apache style, but that can easily be fluffed too especially with a decently long sling. I had an ex cricket bowler try this and he was getting pretty nice distance with this. Comparable or better to what I can do with apache- though I'm not great at it.
I taught a few 12-13 year olds I met on the beach once and they picked it up really fast. All managed decent sidearms after not too much practice and one even managed a respectable fig-8.
Ideally I would always teach with tennis balls, but it's not always that practical using ammo that needs to be retrieved- or that can be easily lost. It depends on the location. I just try to stand a decent distance away if a newbie is using stones... and tell them to do it slowly.
I haven't tried to teach greek or byzantine but they could work. Helicopter could work as I think it's quite a natural movement but poor stone discipline and a horizontally rotating pouch is a little scary to be near