General gemstone value?

Diamond, emerald, ruby and sapphire are valued more highly than the others on your list all things being equal. I would also put aquamarine in that group.

Tanzanite is in its own class. It is a relatively new stone.

Then the amethyst, citrine, garnet, opal, peridot, topaz and tourmaline.

Thanks, @Marina, GA. I am in the field and couldn’t have put it better.

Diamonds while highly valued aren’t that rare, their value and price are artificially kept high. Sapphire and Ruby are darker Tourmalines, usually treated to achieve the desired colors of Red and Blue. Aquamarines may be treated but if you can find a gem quality specimen of deeper Blue then that’s the one I’d put my money out for followed by natural gem quality Emerald (pretty tough to find) then deep Violet Tanzanite.

Yes, diamonds are a marketing miracle, created by de Beers. However, that does not influence my pleasure in finding some nice old rose-cuts in a Victorian setting.

Oh, thanks you guys.
I have another question now. Tanzanite, how does it compare to the other stones in terms of durability. Would it be an ok gem to wear in a ring everyday?

@aiwendil: Tanzanite isn’t the most durable for everyday wear, that would be the Sapphire or Diamond’s advantage. I made an error in memory above- Rubies are a shade of Sapphire not Tourmaline. oops.*

So I was right to not trade in my old mine cut and rose cut stones for the newfangled brilliant cuts?
I wonder where my alexandrite fits in?

Old mine and rose cuts are what get to me. The brilliant cuts seem showy and banal to me.

Sorry, one more question (not sure whether I should just make a new question).
@aubepine said that diamonds, rubies, and sapphires are the most durable gemstones. Is that based off of anything other than hardness? If it’s not would other stones like topaz and alexandrite be just as durable?

Topaz and alexandrite are relatively fragile as well. A fine alexandrite showing strong color change characteristics can rival the value of most diamonds of similar size.

Diamonds are the hardest stones (resistant to scratching), but their crystal alignment makes them vulnerable to cleaving. A diamond dropped from a few feet may crack or even shatter if it hits at the right (wrong) angle.

Sapphire and ruby (color varieties of corundum) are quite hard, and while not as hard as diamonds, they are MUCH tougher due to their crystal alignment.

If it’s durability you are after, go for jade (either the jadeite or nephrite varieties). They are far tougher than the other gemstones. In some ancient civilizations, jade was used to make axes and other edged weapons.