A fitness heart rate monitor is for someone who is training to acquire and maintain general physical fitness in a gym or similar environment. For the purpose of drawing up a list of fitness HRMs, those specifically intended for running, cycling etc will be excluded, unless they happen also to be very suitable for general training.
Here is a list of the fitness heart rate monitors that have been featured on this web site. It is not an exhaustive list.
The list above is large as it stands and not terribly helpful. This list will be narrowed down to include the more popular and/or well-regarded ones for each of the following categories.
Note that it does not mean that the other monitors are not worth your consideration. Many of them have other strengths. This shortened list is intended to provide the starting point of your investigation, especially if you are short of time.