Although there are exceptions, gemstones should theoretically be material* that is:
* Most gemstones are minerals, but there are some that are organic e.g. amber, pearl, ivory.
Fashion also plays an important influence. For instance, Tanzanite, while gorgeous, is NOT durable. It is soft and cleaves(breaks) easily. But it is a popular gemstone now because Tiffany's marketed it strongly in the 80s.
How can we identify gemstones? Gemologists usually identify gemstones by looking closely at the stone's physical and optical properties, e.g. color, hardness, brilliance, luster, inclusions, pleochroism, refractive index, heft/specific gravity etc. Advanced equipment such as infrared spectroscopy can also identify stones using chemical analyses.
How to pick a good gemstone? Well, unless you have had some sort of training in gemstone grading and appraisal, it would be difficult for you to differentiate gemstone quality just by reading up. The only way to be able to grade gemstones competently is by learning on the job from a trained practitioner or expert and by getting as much practical experience as possible or by getting a formal gem education.
As a rule of thumb, just remember that the market puts a premium on pure color, balanced tone, good cutting and appropriate clarity level for that type of stone.
Hope that helps!
I LOVE gemstones and taught gemology for several years.