I can only speak in generalities -- Most of these fishes will acclimate quicker and adapt to captive life when they are young. Size matters when you consider the predatory nature of the fish, so that no fish becomes a meal to another. So, a smaller Lionfish might be preferred to start off with.
The Lionfish like to stalk their prey, so they sometimes like to take some time when feeding. Spot feeding the Lionfish will take care of that, until the other fish learn what it is you're doing and then they will try to muscle in on the feeding. Best to feed the tank, then spot feed the Lionfish. During the feeding of the rest of the tank, the Lionfish may catch on and try to eat some of that food. A lot has to do with the training you've provided the fish while it is in quarantine as to how it will get along when the others are being fed.
With the Trigger, the Hogfish should find its level of being assertive. I would choose an eel of your desired size; medium (4") Trigger, small Hogfish, 3-4" Harlequin, and small Lionfish. The 'smalls' should not tempt the eel.
The Harlequin, depending upon individual personality, will range from shy to forward. Hard to be sure what you get when in that mix. It will benefit from the quarantine and if given enough care and time, will likely be less shy but not completely forward.