This might have seemed very obvious to some, but I just realized we have enough information to support this, so here we go.
Gems are ranked based off their actual ranks on the Mohs Hardness scale. Gems on this scale can only be scratched by gems equal to or lower than them in terms of hardness, so having a higher number makes you more indestructible.
The diamonds are the hardest gemstone with a hardness of 10. The disbelief that a Rose Quartz shattered Pink Diamond would make sense, because the only thing that should be able to scratch a diamond should be a diamond.
Both Rubies and Sapphires (Padparadscha included, as padparadschas are sapphires) are 9s. This is probably why Rubies were sent out as bodyguards for Sapphire, and why Sapphire was allowed to speak directly with Blue Diamond. Garnets, however, vary their hardness depending upon what type they are, but all garnets have a hardness lower than 9, which is also probably part of why seeing them fuse was such a disgrace- they combined and became weaker, even though they were almost the strongest.
Alexandrite, the fusion of Amethyst, Pearl, and Garnet, is an 8.5, making her an optimal attack gem, and making Amethyst and Pearl ‘stronger’ but Ruby and Sapphire ‘weaker’.
Next up is both Topaz and Aquamarine with a harness of 8 (although to be more exact, aquamarine has a hardness between 7.5 and 8), putting the two as equals. Aquamarine is obviously very egotistical about this, because she is pretty high up, and this is probably also why topaz is sent out on missions so much.
Amethyst, Peridot, Rose Quartz, Smokey Quartz, Jasper, Sardonyx, Rutile, and Agate all have a hardness of about 7, making Amethysts, Jaspers, and Rose Quartz-s good soldiers- tough but not too tough. Holly Blue Agate shouldn’t really have the authority over Amethyst and Quartz Guards the way she does, but there seems to be a trend with the ego that comes with blue gems working with other gems, as evidenced by both her and Aquamarine.
Zircon is a good 6.5-7.5, making them a slightly higher up but still fairly average bunch for their jobs as lawyers.
Both Sugilite and Opal are about a 6.5, making Amethyst, Sapphire, and Ruby ‘weaker’ as Sugilite, but Pearl ‘stronger’ and Amethyst ‘weaker’ as Opal.
Lapis Lazuli is a 5-6, making her an average gem, and putting her in the place to do the hard labor of terraforming. Rhodonite also falls here, and if we assume that she is a fusion of a pearl and ruby, then its not surprising that she has to hide as it would make a ruby softer and a pearl harder.
Malachite is a 3.5-4, which could be why Lapis was able to take control of the fusion that Jasper thought fusing would make them stronger. Fluorite also has a hardness of 4, which we can only assume to be dragging down the hardness of some of her gems.
Pearls, the walking coat racks of the gem world, fall between a 2.5 and a 4. As such, they are easily bossed around by almost everyone, and are not expected to be able to fight. Bismuths have a hardness of 2-2.5, so they also would not be considered to be able to fight, and this is probably why they are tasked with working on modifying weapons instead of fighting with weapons.
TL;DR- gem hierarchy based on Mohs hardness scale, fusion of different gems frowned upon because the fusion most likely consists of an upper and lower gem, inevitably bringing down the hardness of one gem