Just a quick list of the “preferred” gems by color.

Red

Delicate Living Ruby: +8 Agi

Purple
Shifting Nightseye: +4 Agi +6 Stam
Infused Nightseye: +8 AP +2 Mp/5

Blue
Solid Star of Elune: +12 Stam
Note: In almost all cases, you’re better served just getting a Shifting Nightseye.

Green
Dazzling Talasite: +4 Int +2 Mp/5
Note: In almost all cases, you’re better served using ANY other matching color gem.

Yellow
Rigid Dawnstone: +8 Hit
Smooth Dawnstone: +8 Crit
Brilliant Dawnstone: +8 Int
Note: In almost all cases, you’re better served using a Glinting Noble Topaz overall.

Orange
Glinting Noble Topaz: +4 Agi +4 Hit
Wicked Noble Topaz: +4 Crit +8 AP
Note: The theorycrafting is out there, NEVER get wicked noble topaz over Delicate living ruby. If you’re just hard up on cash and you have a noble topaz sitting around, go for it… but if you’re paying for the gem anyway, get the Delicate Living Ruby.

Note: Just to reiterate, the 3 gems you should really be using the most overall are:
Delicate Living Ruby
Shifting Nightseye
Glinting Noble Topaz

Meta
Relentless Earthstorm Diamond: +12 Agi +3% Crit Damage
Enigmatic Skyfire Diamond: +12 Crit +5% Snare Resist (Stacks with Surefooted)
Potent Unstable Diamond: +24 AP +5% Stun Resist
Powerful Earthstorm Diamond: +18 Stam +5% Stun Resist
Swift Skyfire Diamond: +24 AP +Minor speed increase
Note: For PvE purposes the Relentless Earthstorm Diamond is by far the best choice. The others are listed because you may want one of them in a PvP swap out helm, and they are generally good choices for that purpose