This is a very complex issue, since it deals with EMI/RFI, ESD, and safety stuff. As you've noticed, there are many ways do handle chassis and digital grounds-- everybody has an opinion and everybody thinks that the other people are wrong. Just so you know, they are all wrong and I'm right. Honest! :)
I've done it several ways, but the way that seems to work best for me is the same way that PC motherboards do it. Every mounting hole on the PCB connects signal gnd (a.k.a. digital ground) directly to the metal chassis through a screw and metal stand-off.
For connectors with a shield, that shield is connected to the metal chassis through as short of a connection as possible. Ideally the connector shield would be touching the chassis, otherwise there would be a mounting screw on the PCB as close to the connector as possible. The idea here is that any noise or static discharge would stay on the shield/chassis and never make it inside the box or onto the PCB. Sometimes that's not possible, so if it does make it to the PCB you want to get it off of the PCB as quickly as possible.
Let me make this clear: For a PCB with connectors, signal GND is connected to the metal case using mounting holes. Chassis GND is connected to the metal case using mounting holes. Chassis GND and Signal GND are NOT connected together on the PCB, but instead use the metal case for that connection.
The metal chassis is then eventually connected to the GND pin on the 3-prong AC power connector, NOT the neutral pin. There are more safety issues when we're talking about 2-prong AC power connectors-- and you'll have to look those up as I'm not as well versed in those regulations/laws.
Tie them together at a single point with a 0 Ohm resistor near the power supply
Don't do that. Doing this would assure that any noise on the cable has to travel THROUGH your circuit to get to GND. This could disrupt your circuit. The reason for the 0-Ohm resistor is because this doesn't always work and having the resistor there gives you an easy way to remove the connection or replace the resistor with a cap.
Tie them together with a single 0.01uF/2kV capacitor at near the power supply
Don't do that. This is a variation of the 0-ohm resistor thing. Same idea, but the thought is that the cap will allow AC signals to pass but not DC. Seems silly to me, as you want DC (or at least 60 Hz) signals to pass so that the circuit breaker will pop if there was a bad failure.
Tie them together with a 1M resistor and a 0.1uF capacitor in parallel
Don't do that. The problem with the previous "solution" is that the chassis is now floating, relative to GND, and could collect a charge enough to cause minor issues. The 1M ohm resistor is supposed to prevent that. Otherwise this is identical to the previous solution.
Short them together with a 0 Ohm resistor and a 0.1uF capacitor in parallel
Don't do that. If there is a 0 Ohm resistor, why bother with the cap? This is just a variation on the others, but with more things on the PCB to allow you to change things up until it works.
Tie them together with multiple 0.01uF capacitors in parallel near the I/O
Closer. Near the I/O is better than near the power connector, as noise wouldn't travel through the circuit. Multiple caps are used to reduce the impedance and to connect things where it counts. But this is not as good as what I do.
Short them together directly via the mounting holes on the PCB
As mentioned, I like this approach. Very low impedance, everywhere.
Tie them together with capacitors between digital GND and the mounting holes
Not as good as just shorting them together, since the impedance is higher and you're blocking DC.
Tie them together via multiple low inductance connections near the I/O connectors
Variations on the same thing. Might as well call the "multiple low inductance connections" things like "ground planes" and "mounting holes"
Leave them totally isolated (not connected together anywhere)
This is basically what is done when you don't have a metal chassis (like, an all plastic enclosure). This gets tricky and requires careful circuit design and PCB layout to do right, and still pass all EMI regulatory testing. It can be done, but as I said, it's tricky.
Yes, it sounds like (a little confusing) you have a ground loop problem, and yes they can matter, especially when trying to measure small analog signals. If all grounds tie back to the same outlet strip via relatively short line cords, then it would probably be OK. However, you say that this cryostat thing (whatever that is) is connected separately to building ground, so that is obviously not the case and it's confusing therefore why you brought it up.
In general, it's good to convert analog signals to digital as close as possible to the source, then ship around digital signals. Those are much easier to isolate, like via opto-couplers, pulse transformers, radio, etc. In other words, a old fashioned A/D card in the computer is not the best overall architecture from a system level point of view.
However, look at the A/D card carefully. Most likely it can be configured for single ended and differential operation. This is a case where you want differential inputs. The cryostat thingy may produce a ground referenced signal, but take its ground and output signal as being differential. This will essentially subtract the ground offset from the signal before converting it.
This trick will only work up to some frequency, probably a few kHz or low 10s of kHz. It should work pretty well in subtracting off any ground signal due to 60 Hz or 50 Hz power line return currents accross ground paths in the loop. Sharp common mode spikes can still confuse the diff amp in the A/D and show up as noise in the final output. It's worth a try though. If it's not good enough, go back and convert to digital at the sensor, then opto-isolate the digital telemetry signal.
Best Answer
Yes this is correct. All you need between the two is a single point of reference. Best practice in most applications is a star ground, i.e. connect the digital ground plane to the power source's ground connection and the analog ground plane to the same physical point. The small passage should be capable of handling any current that could potentially flow through it.
This depends on the application. In some applications, such as underwater, the chassis should be electrically isolated from any charge storage element to reduce oxydization. If you want to electrically connect the chassis connect it to earth ground if the application allows.