The origin of the terms “precious stones” and “semi precious stones” is simply a result of a marketing tactic used by people who sold precious stones. This terminology was invented to create the impression that precious stones are more valuable than they actually are. Diamonds, sapphires, rubies, and emeralds are considered precious and all other gemstones are semi-precious.

Generally speaking  the 4 precious stones, listed above, are more expensive than the rest of the list of semi precious stones. Sapphires, rubies and emeralds are all rarer than diamonds and there are 10 Gemstones that are extremely rare. 
There are 5 gems that are worth more than diamonds: Bixbite, Musgravite, Painite, Alexandrite, Grandidierite.
Using common sense you will think that the more rare gems will be more expensive. However, many colored gems that are rarer than diamonds are still less expensive. The white sapphire which resembles a diamond is a cheaper alternative to the classic diamond. 
With the rising cost of living and the growing individuality and openness to new ideas. Millennial are going the non-traditional route when it comes to engagement rings.

If you choose to break free from traditional diamond engagement rings, you will first be drawn and fall in love with the beauty of the color. However, aside from beauty, don’t forget to consider other practical  factors that are important. Your budget and how much money will buying the stone save you, the hardness clarity and durability of the stone, and the cost of labor that will be determined by how hard it is for the jeweler and the setter to work with the stone.

From experience I can say that  some of the most popular engagement ring alternatives are the following colored gemstones: ruby, sapphire, emerald, aquamarine, amethysts, peridot, opal, garnet, citrines, tourmaline. Usually couples are first drown to the color.

Their advantage is that most of them come in many different shades anbd colors, therefore provide many variations.