Adding in my two cents on this list, since I main bard, and raid with it. I disagree with the priority listed here, and it should honestly be something more like this:
Refresh
Tactician
Palisade
Second Wind
Invigorate
Peloton (**4-man dungeon content only**)
Head Graze
Arm Graze
Leg Graze
Foot Graze
Refresh and Tactician, from a support standpoint, are completely mandatory, and not at all optional. That much is certain. Refresh for your healers, and Tactician for DPS/tanks AND/OR as an aggro dump, since Ranged Physical DPS do not have access to Diversion (and since they removed Quelling Strikes). If you have a NIN, it helps to have them Smokescreen you when they can, but still, having Tactician as a back-up aggro dump is still useful. (Plus, can't always guarantee you'll have a NIN in your group outside of a fixed raid group setting where there will almost always be a NIN.)
Palisade is also a good choice, however, its use in the current raid-tier is pretty limited--since most of the tankbusters/major damage are magical (Palisade only protects against physical damage, not magical), it really only has use in V3S for Halicarnassus' Critical Hit (every 150 seconds). Useful in Susano Ex for Stormsplitter.
Second Wind is something I always keep on me, no matter what. You can't really go wrong with self-heals. Invigorate I keep for if I go down or for heavy AOE situations in 4-man content, since you can't expect Melee to Goad you 95% of the time.
Any of the other skills are more or less useless in the majority of content where they would matter. The silence only has real use in V3S for the Iron Giant if you need an LB bar to reach LB3 for caster LB (but you shouldn't need that if you do Animal Farm successfully). The other Graze skills would have only been useful in PvP settings, or in very select instances (off the top of my head, the mini-boss before the last boss in Sirensong--stunning the seductive scream he does). Other than that, they aren't so important to take up a permanent cross-role slot. If they're needed, I would sub out Invigorate, personally, since you have Tactician to fall back on for TP issues (like if you die). I would definitely not carry any of the Graze skills around with me permanently.
Those are just my two-cents.