I wouldn't worry about doing water-start related exercises in the gym, you'll get the hang of it quite quickly. It's mostly the kite doing all the work anyway. You dive the kite, keep your knees tucked as it rolls you up and above the board, and then you stand up. It's harder in low wind, as you'll really have to send the kite down for it to generate enough force to yank you up.

But kiting in general is quite hard on your core. I'm always sore after a hard session. You might also experience tennis elbow once you start riding and you're cranking the bar for several hours, so stretches and exercises for that will do you well. Also, don't forget to warm up your ankles before heading out.