Most of the other stuff was touched on, but there's one point I need to greatly stressed. Unlike games such as WoW, Diablo, Torchlight, Borderlands, etc, COLOR IS NOT THAT IMPORTANT! I have seen so many people use gear that's 20 or more levels out of date because they're insisting on only wearing colored gear.

The most important thing is actually Item Level. This essentially determines the stat caps on gear, and any HQ or non-crafted gear will be capped on all stats present on it (Main stat for the intended jobs, vitality, weapon damage or armor, and one substat) plus one substat that's not quite capped. Ergo, higher item level means higher stats, color doesn't enter into it. Also of note, when it comes to materia you can't exceed the stat caps for an item. Thus, the main stats and the capped substat can't be boosted further, but you can boost the secondary substat or add substats not present on the base item this way.

Where color DOES matter however, is its relation to equip level. Especially early on you'll find that crafted gear has an item level matching the equip level, but that green items from dungeons have an item level slightly higher than their equip level. This also will apply to some crafted green items made using "damaged" equipment you can find in dungeons (and you may notice the damaged base items have a lower item level than their equip level). This only really applies up to level 50 however.

Once you pass 50, color is largely irrelevant. You'll have crafted whites and dungeon drop greens with the same ilvl increase with each equip level increase, only difference being one level has just crafted items and the next has just dungeon drops. There's also the level caps for each expansion (50, 60, 70) where item level keeps going up with each patch for the expansion while staying at the same level. So, for instance level 50 gear ranges from ilvl 50 to 130. Just get the highest ilvl you can feasibly get (Poetics tomestones work wonders for this at 50 and 60).

So, that whole spiel given, the way I list colors is as follows:

White: Common craftables.

Green: Uncommon but not special. This gear just exists, nothing really special to it, but requires dungeon drops or special gathering nodes that are only up occasionally to craft it, if it's not a dungeon drop itself.

Blue: Lore items. These are either quest rewards or raid drops, or obtained via tomestones, and they always have some lore attached to them. Whether it's the old equipment of a hero of your job, the masterworks of a once-great smith, or ancient allagan armor, every piece has a story and a purpose.

Pink: Aetherial items. Ok, not all of them are "aetherial" in name, but most are. These have random stats but they still follow the rules of typical gear (Full vit and main stat for the job, one substat at full and one at a lesser amount), it just picks two random substats to be the main and secondary. Aetherial gear also gets a bonus to spiritbonding. Each aetherial gear is based on a crafted piece, though the equip level will be adjusted to match the content where it came from (dungeon or guildleve). Later gear from the Diadem does the same thing, though the appearance is also randomly generated.

Purple: Sentimental items. As mentioned before only two types of items qualify, relics and wedding rings. Wedding rings are a statement of one's love, while relics require an immense devotion of time and energy to complete, and thus usually have great value to their owners outside of their effectiveness.