Genetics has gone in a few years from being an obscure, almost academic science to perhaps the biggest single area of scientific advancement in recent history. Whole new biological concepts which didn't even exist 20 years ago are now been turned into practical medical processes, and this science is itself only in its early infancy.
Geneticists are actually biologists. The academic training tend to specialize in particular branches of biology, but follows the same basic academic stream in its early stages and then branches out into specific genetic studies.
At its practical employment levels, genetics is essentially a graduate level science, requiring a very strong knowledge base, lab experience and familiarity with a very wide range of technology and systems used for testing, research and product development.
Career progression in genetics is difficult to quantify in some ways, because this science is itself expanding and diversifying very rapidly. For example, stem cell science is one of the major areas of development of genetic science, and at this stage, nobody even knows how stem cell science itself is going to evolve.
In broad terms, career progression in genetics is developing on the basis of specific areas of expertise, research capabilities, qualifications, published papers, and very much in areas of individual preferences. That's important, because like all sciences, genetics tends to attract people on the basis of specific areas of interest, talents and personal skills.
This is one area where postdoctoral work is extremely important both in terms of career advancement and skills development. Much of the important, groundbreaking work being done in genetics is done on this level, with a large contingent of postgraduates involved. These people are the next generation of geneticists, and that is actually a pretty accurate picture of how career progression in genetics operates.
Genetics has been rightly called a science of breakthroughs, and indications are that the science will expand exponentially along a very wide range of specific diversifications. If you're looking for a career which will challenge you, excite you and keep you fascinated forever, genetics is probably the career you need.