Descrete Fourier Transforms - Resolution vs sampling duration

[mark03]

I have a signal, which is continuous in the time domain, however, it contains "frequency" information that i am interested in and "Noise" that i am not interested it.  The signal and the noise has a range of between roughly 5 Khz and 20Khz, and the exact frequencies i want to monitor for amplitude are spread in this range.
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Having done this, what i then want to do is to transform that time domain signal into the frequency domain, with the best resolution possible (ideally around 100Hz wide bins).  Doing this allows the "user" to identify the fundamental and harmonic(approx 3 of) components of the signal, and then the system will look specifically for the amplitude of those components.  ie initial sweeps are wideband, then to minimise processor load and data reduction,  a few critical sampling frequencies will be chosen.

It's worth mentioning that the DFT may not be the best tool for this task, although it is probably the best way to get started.  If you already have a model of your signal, which consists of noise plus a discrete number of sinusoids, then other techniques with whimsical names like MUSIC and ESPRIT (google it) are better.  The catch, IIRC, is that your model needs to be accurate, i.e. you need to know a priori how many sinusoidal components are in there waiting to be identified.