The types you would need the most are:
- Fire (for Jasmine)
- Fighting (for Pryce)
- Ice (for Clair)
Pryce and Clair both have a Pokemon that isn't "their type". Pryce has Seel and Clair has Gyarados.
That's why I would recommend an electric type, too. Just to deal with those two as well.
Make sure that if you are using a Fighting type against Jasmine it is a special attacker, or just use a Fire type. Steelix is a beast in physical defense. :P
Hope I helped.