Should I have a handful of stretches I keep on repeat or try new ones (more or less) everyday?

I think it is better to have a routine for a set amount of time. But I think it’s good to change it on a weekly or monthly basis but not daily

Both is awesome for your body and muscles! I prefer doing different streching practise every day, without any particular order. I try to listen to my body and follow what feels good. Also following exercise plan is a good idea (if you exercise), meaning that if your exercise was focused on your legs, you're going to focus your streching to your legs.

I don't have any specific stretches that I do. I just stretch what my body feels I need to stretch that morning and focus on that.