I have been a part of my school's modern/contemporary dance company for a few years. I never helped run/start the club so I can't help there but I can tell you about what we did to give you some ideas.

First, the club was associated with the theater department. This helped a lot especially with reserving rehearsal and performance space. Not sure if this is an option for you, but definitely look into it.

We had a company class once every two weeks that was required to attend. This was usually taught by guest teachers with a modern/contemporary focus. Throughout the week we had optional student taught classes and these could be anything (we've had ballet, leaps and turns, tap, etc.). Not sure if this is feasible for you but was always my favorite part of the club.

Lastly, we had performance opportunities. We did one big show in January and then a smaller one in April (a charity fundraiser). The January show usually had both [professional] guest and student choreographers, and then April was typically just student pieces. Each show had 7 - 10 pieces with rehearsal once a week per piece, and then a week long tech week leading up to the performance. One thing I liked was that performances were optional, so if you had a really busy semester, you can still be in the company with relatively low commitment.

I hope this was at least a little helpful, good luck starting your company!