I hope my response isn't too late.
SMN pets are one of those things that make this job so tedious and rewarding to play. A lot of what I'm going say is based on my own opinion and based on my experience playing via PC.
Your pet should ALWAYS be on obey. I find that if you take that split second to swap between Obey and Sic, your egi will pop all their beefy cooldowns. Also, when your pet is in Obey you can use "Heel" to have them swap targets, without risking them auto-popping their cooldowns.
With Egis being in Obey all the time it can be really frustrating if you aren't used to micromanaging. It takes some time to get used to but I find that it's 100% worth the hassle of KEYBINDING your pet abilities/stance/orders. I have "Heel" and "Place" bound, a macro that lets me swap my egi from "Guard" to "Steady" and vice-versa (so nice for those speed runs!), and their 4 abilities as well. I feel like clicking on abilities takes my eyes away from the encounter too much and I'd rather just bind it.
Also, each encounter and group will have different set ups and mechanics that will help you determine which pet is best to use. Does the fight have a lot of adds? Both Ifrit and Garuda have nice AoE dmg abilities. Does the fight have lots of physical AoE dmg? Consider using Ifrit since you can pop his Radiant Shield which in turn will make him do more damage! Is your party made up of mostly Mages? Consider using Garuda since she has no auto attack. If you have Warrior Tank or Ninja use Ifrit! His auto attack damage will benefit from the slashing debuff those jobs provide! Got a headache yet? Hahaha, I do. :[
Like others have mentioned in their replies you should have "Spur" and "Rouse" separately seeing as you can use "Rouse" twice as often as "Spur" and it also has great utility for keeping your pet immune from many status ailments.
"Quelling Strikes" is definitely worth it. It's your saving grace. If you know you are about to nuke a target with Raging Strikes, go ahead and pop that Quelling Strikes too. Would be sad to have all that Raging Strikes damage get you killed because your Fester crit for 2500 and now the boss is smacking your face in. :[
I can't really think of anything more; partially because my brain is mush now. x_x. I hope this kinda helped more than confused.