General professional training is what one undertakes following completion of med school and foundation years -it is the generalist training in a broad branch of medicine, such as adult (internal) medicine or paediatrics. This is currently done by applying for SHO jobs, but in the near future will be the early years of run-through or seemless training (see
www.mmc.nhs.uk).
During this time you will complete your basic post grad exams such as MRCP or MRCPCH before entering training as a clinical geneticist, or whatever other specialty grabs your fancy.
I would be wary of setting your mind on one career before even starting med school -although you may have some experience of a specialty, you ahve little to no idea about the range of medical specialties, what they entail and what in the end is right for you. By all means look at possabilities, but seriously get your general training sorted first before choosing a specialty.