I can understand your concern. Depression is a very serious condition and gets worse without treatment, so I'm glad to hear that you have helped your son make an appointment with his doctor. Is this doctor a psychiatrist or a general practitioner? Either one would be able to prescribe antidepressant/antianxiety medication, but usually a psychiatrist would be able to do a more thorough assessment of your son's depression and his needs regarding medication.
As for the medication, most SSRIs (selective serotonin reuptake inhibitors- a class of medications used to treat depression and anxiety) work very well for both depression symptoms and anxiety symptoms but some are slightly better at relieving depression while others are slightly better at relieving anxiety. So, to answer your question briefly, no medication in this class would harm your son (the side effects tend to be very minimal and include things like fatigue for the first week or two, change in appetite for the first week or two, and/or vivid dreams, etc.) and any of them would probably help with his depression. This class of medications includes drugs such as Prozac, Zoloft, Paxil, Celexa, etc. They usually take about 3-4 weeks to feel the full benefit of symptom relief, so please help your son be patient.
It is also very helpful for people with depression to work with a therapist. This can help them understand why their depression arose, how to cope with it, and how to prevent future episodes. I would encourage you to help your son get an appointment with a therapist even if there is a wait list. You might also ask him if there is a counseling center at his graduate school as many schools have psychologists on staff and there tends to be less of wait list in this type of setting.