My perspective is that as someone who trained in IM and then allergy/immunology at a very large institution with a large peds hospital as well as large adult hospitals.
OP, do you know what a medical geneticist does as far as day-to-day work? If not, I would make sure you shadow one closely. If you really want to practice full time in that setting, pediatric or med-peds makes the most sense. Although, coming from a field like A/I, I think good fellowship training results in both IM and Peds trained docs that are very competent and comfortable with all ages. I've seen some interesting practice settings. Where I did my IM residency, we had an adult trained genetics doc that saw quite a few of functional illness types and ended up working up ehlers danlos and stuff like that and then she'd refer them to a bunch of subspecialists who learned to dread those referrals. During my fellowship, I pretty much never saw a geneticist involved with adult care (at least in immuno) but I often saw them consulted in pediatrics. The consult was usually prompted by either family history, + new born screen, or suspicion that what we were seeing had a syndromic feel to it. I do think it's helpful for the families to have a geneticist involved. It was somewhat helpful as an immuno fellow because these patients often require multidisciplinary care. Although, I never asked genetics a question once and I never had them actually manage the disease. It was more just an interesting note to read. It seemed like they sort of functioned in an adjunct primary role, sort of like they were there to make sure all the necessary parties were involved.
I would question if the clinical role is being phased out more and more with the easy access to genetic testing. Companies like invitae make it super easy to get genectic testing done on patients and most of us in our primary field (immuno, neuro, rheum, onc, etc.) know enough that once we have the syndrome diagnosed, we can manage our part. The days of needing a true clinical geneticist to examine and syndromically identify genetic disorders seem numbered to me. Even in my private practice suburban clinic, I can easily have genetic testing back in a week or two with concise explanantions of any identified variants or mutations and I can always call Invitae and speak to a phd or md/phd type for clarification if needed. We even used to tease the clinical immunologist that he was just thoughtfully working his way to the inevitable invitae panel (...reminds me of the great cardiology diagnosticians prior to readily available echo and other cardiac imaging). I imagine the pay is absolutely terrible when compared to other fields since I don't see how genetics drives any significant revenue (academic pay for allergy is atrocious as well but we can easily bail to PP). It's probably a necessary cost a large institution in order to be accredited or reputable for all the various multidisciplinary stuff. I do imagine there's quite a bit of opportunity in industry for MD/PhD genetics experts but I just question the purely clinical roles. My guess is that you generally would be limited to very large institutions with a low floor and ceiling for pay.
I don't have any firsthand experience as a geneticist though so I'm happy to stand corrected. I would be curious for the two posters above who seemed to know more inside baseball...what does your day to day look like in terms of work as a medical geneticist? How do you contribute to the care of a patient differently than say a phd geneticist or genetic counselor? What kind of jobs are available? That's probably what the OP should be focusing on.