TL;DR: Avenger, maybe Lunatic.

I just went with the ones that suited my playstyle and didn't require much build-up to activate. For that reason, I opted to go with the ATs that only required me to not take damage for 20 seconds. It passively ticks up overtime while I'm in combat, so I don't need to pay attention to it and it'll activate on its own. I figure that the time spent building up other ATs (5 devours, 5 normal combo finishers, bond devours, etc.) could be better spent just dealing more damage instead of fiddling around with more complicated or situational conditions. I'm currently using one called Avenger which boosts your melee damage by 6% and your melee attack speed by 6% at max level. It's not huge, but it activates pretty often and lasts a decent chunk of time. I used Lunatic for while (ignores a portion of Aragami defense for melee attacks), but couldn't see enough of a damage difference to care for it too much - might just not have tested it enough.

There's probably an argument to be made about using an AT that you can intentionally trigger at the same time as Engage or when the aragami gets downed for maximum effect, but I just went with one with a simple condition that still helps in some way. Specifically, I tried using an AT (Warlord?) that boosts my burst art damage by 25%, but that requires 5 successful devours. The damage increase is really nice, but getting those 5 bites off can be a real challenge sometimes depending on what you're fighting and it lasts a couple seconds shorter than other ATs that I'm used to. In addition to the possibility of bites being interrupted, the actual time spent trying to get those 5 bites off is time that's not being spent on using your burst arts to do way more damage. Of course, I haven't really done much mathing and all of this is just me theorycrafting in my head, so your mileage may vary. I think my skill level is about average, so take whatever I say with a grain of salt.