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.
All active components should have decoupling capacitors. The PCB traces between your part and your power source act like parasitic resistors and inductors, and if you don't decouple your ICs, then when their power requirements change quickly - for instance, when they try to change their output signal in response to something - the changing power requirements will cause voltage drop and overshoot due to the long PCB traces. A nearby decoupling capacitor eliminates that high frequency noise by providing for those short-term spikes locally.
0.1uF capacitors are a reasonable default for decoupling; if your device may have particularly large power draw requirements, you should add a 1uF or larger capacitor in parallel.
Regarding grounding, you will find a lot of conflicting advice on this on the Internet. Split ground planes are often less simple and more problematic than you might suppose, because return currents prefer to flow on the reference plane underneath the signal trace. If any of your traces cross the split in the ground plane, you will force that current to deviate around the split in the ground plane, causing a lot more noise than you might have eliminated by splitting the ground plane in the first place.
This article provides an excellent description of why you should consider using a single ground plane combined with careful routing.
Best Answer
It's pretty easy to shoot yourself into the foot with creating splits in the ground plane. Check this for example:
maximintegrated.com/en/app-notes/index.mvp/id/5450
Never ever cross a gap in ground plane with high frequency line! Your layout has several traces going over the gap.
Usually a "moat" would actually look like a horseshoe and go around analogue part to keep the digital return currents away while allowing analogue currents to pass normally. If you put it around the digital part, the high frequency return current noise will (still) take the electrically shortest route to a power source which may cross your analogue bits.
Here's an idealised situation where the AD circuits are all on the same edge. But it'd work the same even if they were in the center of the PCB, DGND would extend all around. Just imagine the image border is in fact your digital ground plane edge with the AGND squares carved out of it.
Actually that image would lend itself into a simple partitioning.. http://www.ti.com/lit/an/slyt512/slyt512.pdf
Note that low frequency and high frequency currents behave differently.
Basically you have created this situation, digital traces going over ground gaps is not nice.
Don't forget you've got several layers to play with. Move digital GND copper to the other side of the board, next to bottom layer. Put digital traces on the bottom layer and now you have nice solid return path for the high frequency noise. Or vice versa obviously.