Photodiode selection for fluorescent probe
See the spectra for the probe. The absorption peak is near the emission peak. 

You want to excite near the peak of the absorption, and detect near the peak of the emission.

The design process goes like this: 


This this an epi-fluorescence arrangement or something else? (epi fluor is where you excite from the same side as you detect) Having all the equipment on one side of the sample has advantages.
Shop for a source. A laser is the usual as it's bright and has a high etendue. Relatively monochromatic. However they are not available in every wavelength (close to the absorption peak). More complex to drive (and perhaps cool).  An LED on the other hand has a broad emission,easier to drive, and available in more wavelengths.
Shop for an clean up filter. The cutoff wants to be near where the dye excitation / emission responses cross.
If a epi system, you'll need a dichroic mirror. 
Shop for an emission filter to detect light in the emission range only.
The photodiode is the least of your worries. 
If the fluorescence signal is small (it will be cause you want to look at small samples, few molecules of the dye) you might need a lock-in amplifier.
A way of confirming that it's fluorescence of the dye and not stray light being detected.


The 3 mm gap to the sample is a problem. You might need some optics to excite a small volume and similar optics to capture as much of the fluorescent signal.

The filter people are Chroma, Omega and Semrock (Edmund Optics and Thorlabs do a limited range) and you need to be aware that there is a limited acceptance angle for interference filters. It's easy to spend a few $k on filters.

The design problem is mostly shopping for sources and filters.

This is the same problem as fluorescence microscopy so google "dichroic filter fluorescence microscopy"