700AGL for the turn is fine, and from what I taught and what was accepted where I was, was a 400' turn. Reason being it kept you closer to the airport, and also 400' is the accepted standard for a turn-out on a IFR departure.

Class-C airspace, you should never contact the tower before talking with approach. The tower's control area is only a small portion of airspace surrounding the actual airport, the approach controllers handle everything else. This is their job, so there really isn't any other way of going about it, unless there's a "Special" procedure for your airport with the tower/approach to do otherwise.