Gear with any crafting stat, Craftsmanship, Control, or CP, will always convert into one of those three. It's always a 1/3 chance to turn into Competence/Command/Cunning regardless of what stats the item actually has. An item with only Control has the same chance to turn into a Command materia as one with Control and Craftsmanship.
The same rule applies for gathering gear with an even 1/3 chance as well. Note that gear with crafting AND gathering stats like Steel Goggles (something like control and perception) will only turn into crafting materia. I haven't tried every mixed piece but all with 2 stats follow this rule. I know there are some chest pieces with 4 stats but I haven't tried them.
Battle gear is a huge pain to convert because it seems to have an even chance to turn into virtually every stat that isn't crafting/gathering. Due to the overwhelming number of elemental types this means you'll end up getting a ton of crap Fire materia and Wind materia instead of crit/determination etc. I'm not even sure if they are split between Magic and War stats because I can't stand converting these. I've done very little testing with them. As an aside, Aetheryte Rings were apparently tagged incorrectly and do NOT give crafting materia. Instead they give battle stuff.
Now, onto the more important stuff:
-HQ gear bonds 25% faster than NQ
-Melded gear bonds faster than non-melded gear
-The more melds the item has the faster it bonds
-The type and rank of materia melded into the gear does not affect the bonding rate, only the number of materia
-The type and rank of materia melded into the gear does not affect the conversion results at all. Neither does HQ vs NQ
-The number of 100% success melding slots in the gear doesn't affect the bonding rate, but it does make them easier to load up with garbage materia (the only use for elemental materia)
Level 1-29 items (item level, not equip level) always convert into rank I materia. They also can only be melded with rank I materia.
Level 30-44 items always convert into rank II. They can also only hold rank I or II.
Level 45-50 items always convert into rank III. They can hold rank I, II, or III.
Level 55+ items always convert into either rank III or IV. The percentage chance to get rank IV is very poor and it's somewhere around 10% for 55 gear. I've never converted any 70 gear because there are no 70 crafting/gathering pieces and my 70 battle gear is stuck at 1%. I don't raid so it will never reach 100%.
Ok so how do you actually bond the gear? If you can equip it as a battle class the easiest/cheapest way is to just throw it on and kill stuff. You can use it as an excuse to finally level your chocobo or if you can convince people to run AK/WP with you in full patricians gear be my guest. You can also bond by crafting or gathering.
Don't be silly though. You can't max out your lvl 55 gear by quick synthing lvl 1 leathers or gathering fire shards. The level of the item you craft/gather (for crafting the recipe level) has to be within 10-15 levels of the gear item level to gain any significant bond.
As a final note the brackets 1-29, 30-44, 45-50, and 55+ all correspond with increases in bonding time as well. 1-29 gear bonds the fastest, then 30-44 and so on. The jump from 45-50 to 55+ is huge. Crafter AF (lvl55) takes TWICE as long to bond as Patrician's gear (lvl50).
Of course I know more and I know the best methods but I can't give away all my trade secrets lol! This should be more than enough to get you started in the right direction.
OH I ALMOST FORGOT!!! The ring in the top slot gains spiritbond just slightly faster than the ring in the lower slot. Don't ask me why, it's probably a programming error. If you equip two identical rings and bond them to 100% the top ring will almost always finish 1-2 crafts/gathers/kills before the bottom one. Also, + spiritbond gain sucks. The only item worth using is the meteor ring with +3 if you're too lazy to make 2 rings to bond. I'm pretty sure they give a flat % increase. Yes I have tried equipping the GC neck, wrists, an Aetheryte ring and the meteor survivor's ring for +6 gain and it's a complete waste of slots.