So many things to do so little time. Basically the KoJ needs all of the cities listed for one reason or another.
Edessa is nice to have, mostly for preserving their army of Armenians and Christians. It wasn't a very good army, but the kingdom needs all the help it can get. Problem is Edessa the county isn't a sustainable state without capturing the fortress cities, since the Muslims can keep marshalling armies at Aleppo, Raqqa, and Mosul. So helping Edessa probably means trying to capture Aleppo.
Which is going to be great if it works out, but there's no indication it might go any better than the siege of Damascus (which the kingdom is still going to need sooner or later anyways).
Ideal would be if they can kill Nur-ad-din and rout his army in a field battle outside Aleppo before a siege, then capitalize that on to take the city itself. Unlike Mur-ad-din, he never shyed away from battle so I think that's plausible. There's other possible invasion points still, but it's a start, and more importantly killing Nur-ad-din removes the single most dangerous person to the kingdom at the time, as well as the most vocal anti-crusader.
After that the crusade probably has one shot left to shoot (they were able to try and attack Ascalon after the failed siege of Damascus historically), so maybe a short campaign against Hama or Edessa proper. Cause again, it would be nice to have.
Now yes, Ascalon is vital to the kingdom, but it historically falls to the crusaders in 1153 anyways. By closing the northern front via Aleppo, this allows Amalric to focus fully on his campaigns to turn Egypt into a tributary, and removing Nur-ad-din prevents the disastrous Battle of Harim if we presume the presence of the crusade in the north also has some knock off effects on the long term strength of the lords in the region. The dude haunted the crusaders for the next 28 years after the Second Crusade, and he also gave rise to Saladin. It's worth it just to kill him. And then you get Aleppo, Hama/Edessa, a peaceful northern front for about a decade, Ascalon, and Egypt as a tributary on top of that. It's a good position for follow up campaigns against down the line, maybe even scare Mur-al-din in Damascus into re-allying with the kingdom since both Egypt and Syria will be undergoing succession woes and leave him with no alternative source of aid.