You should build a priority system for your cards knowing that the priority system can shift at any moment during the fight depending on what is happening and how you wish to slot a card where. While the most obvious card is Balance and the second is arguably Arrow, the remaining four cards are situational and should be used / RR'd / Spread when appropriate.

Just a few pointers:

Arrow
This is a DPS booster and you almost always want to be using it on a DPS - preference goes to those that have native Attack Speed modifiers such as NIN and MNK as the more attack speed they stack, the faster they go. WARs in Deliverance can make use of this as well to eck out more Fell Cleaves and any job going through a burst rotation at the time you give them this will probably get one or two more attack under their buffs. This card will have a lesser impact on DoT jobs like SMN as DoTs aren't affected by attack speed. You may want to refrain from using this if you notice the DPS you want to put it in is low on TP as they won't be able to make full use of the card if they don't have the resources to maintain the attack speed.

Generally good to spread at the beginning of the fight in a pre-buff scenario, though Balance is a better choice overall. If you have no one to use it on, Royal Road'ing for Extend is a good option to.

Great with Enhance on an Attack Speed DPS, though both Extend and Expand are good too.

Balance
Always good, give it to your best DPS and let it rock. Straight forward and easy. You'll pretty much always want to Spread this at the beginning of a fight or if you know the DPS won't be able to make use of the full duration due to long invulnerability mechanics. The only time you should RR this is if you have nothing else to do with it at the time.

Pretty much good with all three RR types - Expand, Enhance, and Extend, though you might not get the mileage with Enhance as you would with Expand and Extend.

Bole
I tend to RR this, though keeping it on Spread isn't necessarily bad either if a tank buster is coming down the tube in the near future. This is indirectly a resource saver as it'll reduce the HPS requirement for 10% for the duration of the buff. You generally don't need to keep this on any content aside from bleeding edge progression. Admittedly, Diurnal Aspected Benefic + Helios + Bole + Collective Unconsciousness on a tank during big trash pulls is pretty fun to watch.

Enhanced Bole + Time Dilation is a nice 15% reduction for 45s and Extended Bole is a resource saver in general. There will be few opportunities to make use of an Expanded Bole so I wouldn't count on it to help with Raid damage.

Ewer
I prefer to RR this, though some ASTs prefer to keep on in their Spread at all times for MP recharge. This is preference though - I tend to almost always RR it or if I have an RR I want to keep, put it on my Spread to use shortly after my next draw.

You'll want to try to combine Ewer with Extend. Enhance doesn't help when Extend does it better and Expand is only useful if it hits three targets (and even though, someone may need the MP much more than the others).

Spear
I pretty much regulate this to Royal Road bait unless I happen to have it line up with some of my other CDs at the time of the draw. If I can't RR due to RR slot being saved already, jobs with short oGCD abilities can make use of this such as DRGs, NINs, and MCHs. Some ASTs would prefer to spread this for use of their own cooldowns later down the line. I personally don't like this but if that suits your playstyle, go for it.

Enhance is the best RR to go with this if you must use it. 30% reduction on CDs is a pretty big number, especially on some longer CDs. I find Extend pretty bad though it may allow the player to clip more CDs with this ability. The only time you should Expand this is at the beginning of a pull when everyone will be popping their CDs for bursting.

Spire
More or less RR bait unless you just raised a dead Physical DPS. When that happens, you pretty much want this to get them back into the game as fast as possible.

Expand is generally the biggest DPS booster in the game when going for pure damage so this works out well to RR for the next draw. Extend Spire is a solid 30s of TP restoration for someone and should be used in those rare opportunities that it's useful. You generally shouldn't need to Enhance or Expand this, and should try to avoid doing so.

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In general, the best ASTs are those that don't follow a rigid system of rules when using their cards. While there should be an overarching goal you want to achieve with your card selection, sometimes RNG won't allow that. In these instances it's important for the AST to understand where they and their party are in the fight and how best to use their cards to suit. Sometimes, the best thing to do is just let the Draw expire and move on to the next.

I personally tend to use Spread as a 2nd Shuffle - if I get an undesirable card for my current RR scheme and Shuffle nets me nothing, I put the current card in my Spread and just wait out the next Draw. This way I can drop the card from my Spread later if need be after consuming the RR with my next Draw, or use my current RR with the current Spread then RR the new Draw. It's a bit complicated to think about, but there's a large array of actions an AST may employ to try to push RNG into their favour or at least minimize bad RNG impact - this comes with experience of playing the job.