What is a good wiring configuration to minimize noise on an analog DC signal?
You have to establish the precise nature of the system noises in terms of how they might superimpose on your signal and you need to do it for each cabling scenario to get a definitive answer. But, it doesn't sound like you know the numbers so you then have to decide what are the likely better options.

The likely worst option is plain ordinary untwisted parallel wires. The better cabling solutions are coax and twisted pair with a screen over the twisted pair being the potentially best candidate but this requires balanced differential signalling down the cable and this may be as complex as the best solution which is to fit the ADC up at the photodiode.

Even with the ADC up at the photodiode you might need to improve things by opto-isolating the whole thing (power and data) so that there is very little influence that noise can make. Check out ADI's set of digital/power isolators - I think they are called ADuMxxxx where xxxx is the number of the various parts they offer.