Longtail cast on with doubled needles - I'm holding two needles parallel to each other and form the sts around both of them.
I know, this doesn't really add additional stretchiness but it is the way I learned from my grandmother and she was the best sock knitter ever (and I'm totally objective here 😉).
For socks I actually care more for function than for looks - if the cast on looks a bit sloppy before I put on my socks: don't care, they need to fit when they're worn.