All the magics work on pets. You should have a lesser Hiryu with each magic. Then advance to a Cu and then horses. Then the new drakes. Reptalons. Thats why they sell stable slot increase tokens.
The first "magic" Discordance: Thats is what it does. It Discords things.
Magery - Works great on things that have it naturally. Casts magery spells. Teleport is not always wanted, if you add the mastery you get that. They bless themselves, heal and cure, which allows them to be self sustaining in small crowds so the Tamer can also kill things or do damage. Too expensive to add to other pets.
Thats the key, heal and cure for defense which turns into offense because your pet stays focused on the target and hits faster and more often than one that is damaged. And they can fight on their own longer while you kill what needs to be killed. So My list is biased upon that. Here are my rankings.
Chivalry: Heals, cures, removes curses!!!! And they use their Chivalry damage modifiers to increase damage. When they have EoO on you cant let them have 20 different mobs on them. Walk up, mount the pet and drag a smaller crowd away to annihilate them.
Mysticism: Heals, cures, removes curses!!! They throw rocks at targets!!!! You gotta have one of these!! They use the area damage mystic spells. They make soothing nature noises.
Magery: (See above) I think the damage level of the spells makes it fit here.
Spellweaving: They cast the damaging Weaving spells. They cast WoD with no regard to the targets health.
Necromage: They do the magery abilities!! But then they do the corpseskin on themselves.
Necromancy: They cast damage modifiers but they cast Corpseskin on themselves. BAD. Has potential. Put it on a Ram or Tsuki Wolf. They make a candle lit picnic area for you.
Only Tokuno pets can get the real version of these two magics: I rank after magery.
Bushido: They use their damage intensifying spells. I don't notice any confidence. They use the skill based defense increase and defense spells. We built these first, they worked great until we saw Chivalry damage.
Ninjitsu: As soon as you put the magic on, the pet gets 100 hiding. They use the Ninja damagers when coming out of stealth mode. Hell ya you gotta have a pet that can hide and make Bruce Lee noises!!
They all do more damage than a pet without them would. Make a few different type pets of each magic.
Things you can put magics on.
Hiryu
Cu Sidhe
Equines
Reptalons
Cold, Crimson/Platinum Drakes
Other Flappy Pets.
Someone else can go into more detail or add specific spells. Or dispute the order.