48 years ago - Julian Gregory Day is born.
23 years ago - 25-year-old Julian commits his first murder, which becomes a series, all based on various interpretations of the calendar.
18 years ago - 30-year-old Julian is found by the Falcone family and kept on retainer as an assassin.
11 years ago - 37-year-old Julian is paid by Roman Sionis to kill Sal Maroni in prison. He then escapes along with Drury Walker and accepts a contract from the Oswald Cobblepot, meeting with the Johnathan Crane to torture & kill Carmine Falcone's son, Alberto Falcone.
3 years ago - 45-year-old Julian escapes Arkham during No Man's Land. He takes over a courthouse before he is stopped by Harvey Dent, who plans to kill him before he is stopped by Comissioner Gordon.
Calendar Man's status as a distant F-list character is pretty well known, but so too is his rise back up to a status that actually gave him a role to play within the larger Batman Mythology. It's interesting, because his status as an incredibly dangerous killer that is kept locked up but will sometimes engage with the heroes and offer them advice on the inner workings of their foes minds is such a huge departure from his original design that they might as well be different characters. It's not even really worth trying to reconcile the two concepts, you just need a way to support his current design and make sure it's a complete character.
Calander Man's Comic History
Calendar Man first appeared in 1958. He staged a different major robbery based on each day of the week, each time in a completely different terrible costume. In later appearances he started staging his robberies around different months, or other calendar measurements. The only real consistent quality of the the character was that he was absolutely terrible. He would only appear when it the story actually required classic characters that were noteable for being aweful.
This continued to be the character's entire schtick until 1996 when Jeph Loeb and Tim Sale created Batman: Long Halloween. Among their many innovations was the idea of making Calander Man a Hannibal Lecter allegory. He spent the entire series trapped behind a glass wall, assisting Batman and Comissioner Gordon through increasingly self-refferential riddles. It was an absolutely genius decision... for some reason the character fit the role perfectly. This has been the central concept for Calendar Man ever since.
Our Calander Man Story
If we're going to do our own timeline, then we get to use a version of Calendar Man that was ALWAYS his more terrifying variant. We can completely avoid the idea that he was staging rediculous robberies in obsurd costumes and just understand him as a comic-version of Hannibal Lecter with a specific theme. His story doesn't begin with him as a thief, it's as a serial murderer. In fact, we took a small cue from the way the Gotham series used Victor Zsasz and actually make him a contract killer for the Falcone family before his imprisionment. His best stories are all tied to the early crime families of Gotham anyway, so we might as well build him into their fabric.
There is a strange conflict moving forward with the character, because the entire visual for him hinges on him being inside a cell in Arkham. If he's ever out and on the loose you really don't get the same character, he basically devolves into a fairly generic serial murderer and Batman already has Zsasz for that. The solution seems to be to actually severely limit the number of times he escapes from Arkham. Let those be MAJOR threats because he's such a prolific killer... otherwise he remains locked up. This actually enhances his menace. We can actually see him regularly serving as a source of information to the heroes because he really is a genius and expert on the psyche of Gotham's criminals... but when he himseld escapes it's terrifying.
Calander Man's Costume
This is an interesting question, because while classic comic Calendar Man has worn some fameously poor costumes and we're clearly never using any of those, and for the bulk of his appearances he's either dressed in a simple suit as a mob assassin or in his prison jumpsuit, there is still the question of his few times having escaped from Arkham and loose in Gotham. Do we actually put him in a costume, then? It seems like a missed opportunity if we don't.
The answer actually comes from a neat place. In the first Batman: Arkham Asylum game you could unlock artwork for a huge variety of Batman villains, even ones that wouldn't appear until later games in the series. Calendar Man was depicted in a red suit with a long high collared coat and a white turtleneck. The outfit had the numbered calendar motif on his shirt and in the lining of his long jacket. It was a very slick look that actually works really well for the modern Lecter-esque version of the character while still looking like he belongs in a comic book.
There is the question of WHY he decides to wear this outfit. When he first escapes he doesn't start engaging in his old habits right away, he instead spends almost a year in hiding. It could actually be that he makes a deliberate choice to step up and join Gotham's costumed villains and show them all how it's done.
Calander Man's Future
Calendar Man's role in the story is to stay locked in his cell, and it's for the best for him to remain there. There are a limited number of real uses for this, though, so it's very likely that this character will fade into obscurity unless someone can come up with some very clever thing to do with him in the future.
The one concept that makes the most sense as some sort of far-flung future use for the character would be as the figurehead working behind the scenes in some sort of incredibly long-form far-reaching evil plan that takes place over a very long time. If, for example, one of the future versions of the different hero teams finds themselves confronted by a variety of different enemies all working together to some far reaching goal that doesn't seem clear to anyone, one of the only characters that would be able to really put that together would be someone as meticulous as Calander Man. It would just have to be some sort of incredibly esoteric goal that would only appeal to someone obsessed with the passage of time.
That being said, it does seem like this is a character that would benefit from having some sort of time-travel ability added to him down the line. We're not doing that, obviously, but you can't help but imagine that he might actually someday make an interesting Kang allegory withing DC.