Same for us too. We usually hack/jump with short ones and school with the longer ones that you can use without taking your hands off the reins. The longer ones are more tricky to use for beginners when you're changing over the sides as you change reins.
I use a schooling whip (long one) if mostly doing flatwork and might be doing bit of jumping. I'd use it out hacking too. If I am working just on jumping or doing a jumping course I use short whip.
You have to be careful with the long type that you do not accidently flick the horse with you are riding and get your instructor to show you how to change schooling whip from one hand to other in proper way when changing rein.
You can get them cheaply enough so you could just get one of each, should only be about a fiver each.
I've been having regular lessons once or twice a week and the occasional hack. Usually the instructor just gives out whatever whip is to hand, short crops or the longer type. Because these are the schools, they are pretty tatty so I've decided to buy my own, but am unsure which type to go for.
What would you experienced people recommend?
I ride a variety of horses, little stubborn ones that need a whack! And more forward going larger ones that don't!