
The 3 Offensive Gemstones (@ a 25% reduced price) 
Question :
Which of the 3 offensive gemstones is the best to add ?
I hope to answer this question in this post. Let me first say that a polished offensive gemstone normally costs 6400 Andermant and not 4800 like in the image above. But today gemstones were on a 25% reduced price, that's why they are labelled as 4800 Andermant.
I will try to answer this question by adding 3 polished offensive gemstones (ruby, onyx and sapphire) at a time to my character and calculate total damage for each gemstone.
In that way we can see which gemstone has to most influence on total damage done. But first let us make a formula to calculate that total damage done.
Formula for total damage per second done

Character values with no gemstones 
In the image above you see my dragon knight's statistics. The Legendary Horns have no gemstones inside, I call this my 'basic' character. Mind that there are 3 (actually 4) values important to calculate damage done.
1) Base Damage : Gemstone > Ruby
This is the damage done with 1 stroke. It has a minimum and maximum value. So you damage done with a single stroke can vary between those 2 value. For my calculation I use
average damage which is the average of the minimum and maximum value.
avg dmg = (min dmg + max dmg ) / 2
2) Attack Speed : Gemstone > Sapphire
The attack speed value gives the number of strokes per second. When we combine the avg dmg (which is the damage on average done by 1 stroke) with the attack speed (number of strokes per second) we get the damage per second. In formula it looks like this :
avg dmg/s = [(min dmg + max dmg ) / 2] * Attack Speed
3) Critical Hit Rate (CHR) : Gemstone > Onyx
While damage and attack speed is pretty straightforward, CHR maybe needs some explanation.
To explain this we introduce the term 'Critical Hit'.
A critical hit is a hit where the normal damage is multiplied by the critical damage. The Chance of delivering a critical hit is given by the critical hit rate.
Now back to my basic character to explain this definition. My CHR is 24.90% and the critical damage (
CD) is 200%. This means that in 24.90% a hits of mine does 200% of my avg damage.
This also means that in 100%  24.90% = 75.1% I deliver a normal hit. This 75.1% I refer to as Normal Hit Rate (
NHR).
Calculating for total damage per second done :
part A : NHR
(100%  CHR) * [(min dmg + max dmg ) / 2] * Attack Speed
part B : CHR
CHR * [(min dmg + max dmg ) / 2] * Attack Speed * CD
Total formula = part A + part B
{(100%  CHR) * [(min dmg + max dmg ) / 2] * Attack Speed} + [CHR * ((min dmg + max dmg ) / 2) * Attack Speed * CD]
Explanation. Part A gives the average dmg/s for normal hits. Part B is the equation for a criticit hit. Mind that the critical damage is added in this part.
Our Base Character
As we calculate the dmg/s for our base character we get :
 {(100%  24.9%) * [(317 + 375) / 2] * 1.18} + [24.9% * ((317 + 375) / 2 * 1.18 * 200%]
 (75.1% * 346 dmg * 1.18 attack/s) + (24.9% * 692 dmg * 1.18 attack/s)
 (306.61 + 203.32) dmg/s
 509.93 dmg/s
Although my character has only 375 maximum damage per swing, it does almost 510 dmg per second. This is possible because it delivers more than 1 attack per second (1.18 to be precise) and because in 24.9% of the cases the damge done is dubble the normal damage.
Offensive gemstones compared
Now that we have our formula for calculation dmg/s, we can compare the effect of adding different gemstones. As you can see in the image underneath, I added 3 polished gemstones (or a equivalent of that in case of the ruby) at a time.

Values for each gemstone 
In the table you can see the values for the different characters.

Calculations for different gemstone additions 
Adding 3 polished sapphire with a total of +15% attack speed seems to give you the most value for money. It raised the dmg/s from 510 tot 583, that's a raise of 71 dmg/s or 14%.
Adding for 19200 Andermant 3 polished Onyx gemstones raises you dmg/s with 'only' 32 points !! That's roughly half (read : 50%) of the effect of the sapphires.
The rubies or somewhat in between. But there is still a 22% difference between the effect of the sapphires and those of the rubies. Pretty significant imho.
Conclusion : Adding attack speed seems the best option if you want to inflict more damage. Adding CHV seems to be the worst choice.
Some remarks
1) CHR increases not linear. When you have an already high CHR, the effect of adding extra Onyx gemstones will be less than when you have a low CHR. I found the image underneath on the German Forum
in this post.

CHR increase is not linear 
2) Adding 30 dmg in gemstones increased my damage with 38 points instead of the expected 30. This the effect of the base damage bonuses you get in the experience and knowledge tree. The higher you are on those trees, the greater the effect will be.
3) Some items (mainly weapons) have enchantments which increases damage or attack speed percentage wise. Adding gemstones of those enchantments will also increase the effect of that gemstone.