Given that we probably won't get any additional information, here is my assessment on the options given:
[ ] Capacity
You could focus on sheer size, making a library that can be conveniently scaled pretty much indefinitely. Your library is always going to be able to grow, but if you want to go completely off the rails and dedicate yourself to collecting literally every written work ever made, this library will be able to handle that without any problems.
Being able to store literally every written work and then some is not just overkill, but overkill to an insane and truly unreasonable degree. The Old World currently doesn't even have access to basic geographic facts about the far east or far west, let alone being able to source translated texts from there by the wagonload. If society ever reaches the point where anything like that is even remotely considerable, said society will also be easily able to just construct a second even grander library.
[ ] Comfort
You could focus on a library that will be a delight to visit or even study at for prolonged periods, with a focus on easy accessibility, well-lit reading areas, plentiful study rooms, private quarters, and built-in taverns and restaurants.
This is maybe the only one where I fear that "reasonable" for Dwarves doesn't much differ from "reasonable" for anyone else. A baseline Dwarven library of import is larger, more secure and better ordered than any contemporary Human library and it is magically enchanted with book protecting runes on top of that. But is it really any more comfortable than, say, the library in Altdorf?
Also look at the text. Most other options mention truly outlandish things, barely conceivable as physically possible without magic. But this stuff here. That's just a normal amount of awesome. Hell, it could be the description of any fancy shopping mall. Except, you know, with publicly accessible books.
So the pros and cons of this option are two sides of the same coin as I see it. On the one hand it might be the largest proportional improvement from baseline. Because while with the other options the Dwarven architects will entusiastically nod along when told to use even more of the budget for the thing they kinda wanted to do anyway, here they might well be going "She cares about what? Well, if she says so we'll just try to reallly really give her what she wants I guess" and go above and beyond on something they might otherwise barely have thought about. On the other hand that also means that we maybe won't see anything mind-boggingly insane by our own standards as players. Just, you know, an awesome comfortable library that's unprecedented in the Old World specifically, but whose other features (Dwarven size and security) still matter more to us than the one we chose to emphasize.
[ ] Holy
Most libraries are dedicated to one God or another, so why not follow the trend? Carve dedications to Verena, Valaya, Quinsberry, and Hoeth into the very bedrock alongside subtle nods to Ranald, and make allowances for large public shrines to the more acceptable Gods.
The main appeal I see for this from a different angle than the reasons I have for liking the other options. With everything else I am drawn by how I see the library from an IC viewpoint, if I were to actually insert myself in that universe and advocate for what I want to have constructed for me. But here I would be voting OOC for what it might do for the story. This option probably has the highest potential to lead to surprises and plot hooks, as well as bringing the struggle of the Gods to the screen and being the one that would most intrigue and involve Cython.
[ ] Order
Despite the best efforts of librarians, practically every library eventually has to resort to The Stacks when the amount of books outstrips the ability to impose order on them. Every scholar has known the experience of delving deep into a maze of dimly-lit shelves many times their height in search of a volume that the library's records insist is in there somewhere. Seek from the outset to ensure that no visitor to your library ever suffers this fate.
I am most torn about this one. A lot of arguments by other players were very convincing to me. Order is definitely vital to any library of considerable size. All else being equal this seems like the most important option. But I am not sure that all else
is equal. I simply don't know if Dwarven "reasonable" amounts of Order aren't already more than enough, the way that Dwarven "reasonable" Capacity and Preservation are.
[ ] Preservation
You could focus from the outset on the preservation of the gathered materials from both natural disaster and the march of time. The masons will use techniques meant for facilities built atop live volcanoes to create a library that could withstand being the epicentre of the beginning of a second Time of Woes, and a great deal of care paid to air shafts and ambient humidity will create separate sections of the library tailored for the different needs of paper, parchment, and papyrus, and a means of completely securing the entire facility such that it could last another few millennia of enemy inhabitation unbreached.
Another massive overkill, if not as massive as the capacity one. At least in Warhammer something like a Time of Woes calamity or a Hold subjugating Waaagh are not at all unprecedented. And while many other players emphasize that it's more important that the library actually serves people before it is sealed due to the fall of K8P, the idea that millennia from now during the second reconquest someone finds an intact library with priceless collections of ancient knowledge certainly appeals to me.
But, well, we already know that K8P's furniture storage was secure enough for the wooden items inside to be found intact. I can't imagine that our library will be less secure than that. Or even than the vaunted vault.
Beyond that, given that this is Warhammer, even this overkill of Preservation is not enough anyway. It probably wouldn't survive an End Times like event, which might well happen within the next couple centuries. And surviving any less total extinction events (of the kind that just eradicates all Order races from the face of the earth) isn't really all that useful either, for all that vampire society might eventually delight in it. And it doesn't even protect from more internal societal calamities or sabotage like Chaos corruption and the like.
[ ] Security
Your personal library is split into three sections: general access, Collegiate access, and completely secret. A larger facility will need a commensurately more complex system. Build the library from the ground up so that there will be different sections dedicated to different levels of access, and in such a way that every visitor will be convinced that the highest level they have access to is the highest level that exists.
The main appeal of this one for me is that it increases the chance of eventually convincing even Dwarven Guilds and mages of differing traditions to store written knowledge here for posteriority. But it only increases the chance, it doesn't do anything like guarantee such an outcome.
Beyond that I don't think I am all that interested in anything more subtle and secure than our penthouse in Karag Nar, special rooms included. In fact, going over board with something like this might have the opposite results from what we'd hope to get by going all out on Order or Preservation. Like imagine if a couple generations from now some guild or organization with their own private section dies out. Suddenly the secret room behind the high security room behind the private room literally becomes nothing more than an inaccessible section of thick wall full of forever lost knowledge. Putting a focus on secure and secretive compartmentalization would also make cross referencing a nightmare as the library grows in size and prestige.
In conclusion, I am split between Comfort, Order and Holy. Comfort because I feel like it is the least likely to be covered enough by the baseline. Order because it matters so much and I don't actually know if the baseline is or isn't enough. And Holy because it might be the most fun story/game wise with the most impact on the Quest itself. Security has pros and cons and thus narrowly loses out to my top three. And Preservation and Capacity seem like unnecessary overkill to me.