Why do you want a 24-bit ADC? That's a very high resolution - what application do you have that would need this? Also not likely that your photodiode's output is that reproducible to come near that resolution, I wouldn't be surprised if the noise level eats up the first 8 bits of your signal, meaning you could get a just as accurate measurement using a 16-bit ADC.
I'd use a high-impedance OpAmp to buffer the signal, so you can read it with just about any ADC. To increase precision a bit you can add a gain to your OpAmp circuit, to get the maximum closer to the maximum of your ADC (e.g. a 4x gain for 0-3.3V, 6x gain for 0-5V).