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As with any profession, one needs to know the very basics. This should come from your basic education and college experience. The details are more often learn on the job, medicine being a good example. Once you master the basics one can manipulate the knowledge to fit new and different situations. Thatis where progress is made in science. Learn the basics!! Learn on the job from there.
Kevin Lam CISSP, PMP, ITIL
Manager, Incident Response
Perhaps, consider laboratory testing such as a career as a Clinical Laboratory Scientist (CLS) that would compliment your interest in genetics. There's high demand for these roles and the pay is great after one gets experience in his/her belt. There are many national labs (Quest, Labcorp) and regional labs out there.
Genetics is such an amazing path, though it can be difficult to learn with so many twists and turns. With a degree in genetics their are many different pathways you can choose. Just because your degree seems limiting to genetics however you can probably get a job in multiple different fields of biology or other sciences. Many of the roles you will probably find yourself in would be in a lab, but there is lots of growth happening in that field as genetics are such a hard thing to pin down and are ever expanding. I suggest just typing in "genetics jobs" in google and wandering down the rabbit whole.
I loved genetics from the time I learned about Punnett squares! I wound up majoring in Cell Biology and Genetics which was similar to a Biology degree with some classes more specific to Genetics. One career I considered was genetic counseling but wound up going into research after joining the lab of my Cell Biology professor and loving it. I went on to get a PhD in Cell Biology where I studied genetics of little worms called C. elegans to study cancer.
There are some really cool jobs related to genetics. For example, consider DNA forensic analysis or plant geneticist. If you go into the medical field, you could be an immunologist or do cancer research. This is an exciting and rapidly growing field. Good luck!