I'm sure there are a number of ways to do this that will reflect the person's shooting style and logistics such as size of studio, outdoor venues available for shooting, etc.
You are right about being concerned about the wide end. A 70-200 will not cut it for group shots, indoors, imo, and not the most convenient for outdoor groups, either.
I would get the 70-200 f4 and team it with something wider. I woudn't be concerned with how fast the wide lens is since speed is not all that important to the type of portraits you are going to be covering, imo. So, as long as it's good at f4 or something similar, go for it.
85/1.8 (for those thin DOF shots)
Something in the 30-35mm range for groups.
That should all fit within your budget.
The wide lens will most likely require you to keep subjects well away from the edges of the frame so get wider than you think you will need, because you will be cropping.