[X] Decompress
[X] Full War Regalia
Winning the tournament is the most important now, right? Brings both the social recognition as well as personal power with Essense. And I'm afraid pulling the punches by investing in a long-term build might not be the best idea against this DB crowd. So upping direct combat capabilities and restoring the energy to better utilizes them seems like the best bet.
For Full War Regalia vs. Sword and Self: short term does not necessarily just this tournament. Unless we go for Stockpile, Ulyssian will have spent most of XP and training time anyway. Unless a time skip is guaranteed (and even if it is), he has too many OP enemies in the here and now to curb his short term prowess so. Both the tournament contenders and the Sids, who won't likely wait for Ulyssian to achieve his optimal build. Actually, there is a big chance of them striking exactly now. Whether at the Academy, in which case the next power-up time skip becomes not so certain, or at Ulyssian himself, with him currently outside of Zao's reach. All the more reason to become as strong right now.
Also, the long term costs of Regalia do not seem higher than those of Sword and Self. It would be one thing if the two choices were even a little close in terms instant benefits, but from the description Sword and Self 'has much less direct combat strength than Full War Regalia', which is the most precious resource right now. Regalia's Evocation, on the other hand, will become available 'much later down the road'. Much can happen during that time.
[X] Ayala
While Cathak Polemgaos is dangerous, he is also a relatively known variable. While the AVOID / ENCOUNTER would still be good to use on him, I doubt the investigation will dig up many weaknesses, or that he indeed has prominent weaknesses in the first place. Too old, experienced and well-rounded character. Better to spend the action on an unknown to get both benefits. I doubt that Cathak is more dangerous than some of the less known combatants. ...And since there is always the possibility of choosing the target worong, even better to maximize the gains by investigating a person which we know has secrets we can uncover!
Also, I personally find the presense of the Infernals the third most interesting element right now (right after the tournament itself and Nilul's hilarity). Learning that they are not DB Exalted looks like a great way to acquire leverage on them, as I doubt they want to be found out. Then use that leverage to, for instance, make Ayala throw the match. I'm sure nothing bad will happen. And of course, interacting with Infernals will in turn most likely affect Nilul interactions...
