Knowing your intended readership, you should have a good idea as to who publishes books for them. You can often see this, for instance, in the publishers listed in your list of references. But do not go thinking there is only ever one right publisher. Narrowing down your choices involves posing yourself several questions. There are other questions too but these ones are crucial.
Small publishers tend to be quick on their feet.
Conversely, a number of prestigeous American university presses are known for taking 3 years to release a book, by which time the topic is no longer as 'hot' as it once was. Speed cannot be achieved at the expense of quality, however. Getting a monograph out in 6-9 months involves a lot of stress and fancy footwork if a proper job is to be done, and it still requires that enough time has been spent beforehand. For instance, any quality publisher will not accept a monograph manuscript before it has been thoroughly reviewed by one or more external evaluators. This process is notoriously slow.