I'm new to Vampire: the Requiem and I would like to write my own chronicle but I don't know where to start. Where can I get inspiration and how can I structure the campaign/chronicle so it's cohesive and feels true to the setting of VtR?
I don't have experience with Requiem. But I have a big load of experience with Masquerade, and general advice constructing a chronicle must be the same.
There are a lot of approaches building a chronicle, but they always start the same way: a simple idea. Like "a weak prince contested by several elders" or "a conflict with werewolves" or "vampires in competion for the love of a single mortal" or even recreate the feeling of a book or movie. So, the first thing you need is that idea.
Then, as I said, you could use different approaches to build the setting. I am going to tell you what I did for my last chronicle.
After I had a first idea of what I wanted for my chronicle, I made a list with the most common themes in vampire literature and films (lust, violence, death, immortality, humanity,...) and I told my players to choose which were more appealing to them. This way I had an idea of their expectations. This isn't always necessary, but I didn't have much predetermined, so I let them set some themes.
Then I added my own, what I wanted the chronicle to be about. Many of them come from the first idea. Also, I visited TV tropes to learn which tropes I would like to insert.
Sometimes is difficult (at least to me) to differentiate themes and ambient. The ambient is for me like some more subtle theme that it's still present in all the setting. It must be underlined on all locations and characters descriptions.
For example, if your ambient is madness (which could also be a theme), all the main characters would have twisted minds, the minor should be desperates, the locations should have loud sounds and consfusing colors, barting dogs and such.
For me, the centre of the chronicle are the characters (NPCs or PCs). So, once settled ambient and themes, I start with characters.
It is often better to start with PC (although at this point you sure would have several NPCs in mind, just try not to concrete them too much). This way, you can build the setting around them, opposed to build first the setting and then try to insert PCs in your already defined world. Remember PCs are the protagonists and the world rotates around them. Pay special atention to the Backgrounds, as they are the PCs' connections to the world.
Once you have your PCs, you can start concreting your NPCs. Make connections with the players (sires, friends, rivals,...). Add the ones you also need to treat your themes, and to fulfill your first idea. Make all NPCs of the characters background: they're not only a resource, they're plot seeds.
When creating NPCs have always the ambient in mind.
Your chronicle will have main plot.
Also you will make secondary plots for treating the themes you came about. The best way to make use of themes is having plots based on them, rotating them, and repeating several times.
You will also need to make personal plots for the characters. Base them on their character personality, history and motivations. Listen your players and you will get cool plot ideas. Try linking them with themes.
You will need to make new characters for some plots, or fit the ones you have into the roles the plots demand.
The prelude serves as the presentations of the PCs. Against the books advised, I don't always make them about the embrace. As in vampire fictions, a character prelude can start with him being a vampire. Three things are important:
A chronicle, like any fiction, should have an end. Better to close themes and plots than let the chronicle die by boredom.
I can't give much advice on this, since I many times fail to follow this rule.
And that's all I can think of without getting in much detail. Hope that helps. And read the books, there are a lot of helpful advice.
In my core book, starting at page 17 they have a list of inspirations/sources for Requiem and it's fairly extensive. If you watch/read even a smidgen of the titles listed, I'm sure that the ideas will start pinballing around.
Without more information about your table and your own ST style I can't really give you much more than that.