New to photography need advice on equipment for portraiture

I have a degree in photography and was a professional photographer for 25 years before changing careers.  There's much more to professional photography than the actual photography.  In addition, the market is flooded by hobbyists like yourself who bring a lot of enthusiasm but little skills to the job.

Shoot for a while as an amateur.  Get a feel for how you want to approach it.  Location baby photography can be done with just a camera, good window light, a reflector and a few props.

Since you are in the market for a camera, I suggest at least a semi-pro one, preferably with a full frame sensor.  I also suggest you use prime (fixed focal length) lenses, with the possible exception of the Canon 70-200 f2.8.  You'll need a 50mm, an 85mm and possibly a 135mm.  I prefer using manufacturer's lenses.

Have fun with your photography class.  I've taught at a local university in their continuing education department on and off for 30 years.