Hi Allen, A can of worms for sure.

I will see if I can describe how I do it in most projects. I generally use a type of buss grounding system. The start of the buss is at the ground terminals of the inputs and traverses the signal circuit generally from front to back ending with the output grounds. I have also used a buss like that connects the input and output grounds directly and then goes out to the remainder of the circuit. I normally use 12 gauge solid copper wire for the buss but have used silver wire on occasion. The power supply (negative side in my tube designs) all connect in a buss arrangement as well and then there is a single heavy gauge connection between the power and signal busses. Often at the point near where the input buss starts. If there is a three wire AC mains I will make a single connection to the ground. It will usually be at the same spot as the the power and signal grounds tie together and is isolated from both by a 120-150 ohm resistor with a parallel type X2 cap of between 0.1 and 0.22uf. If a metal chassis is used, or there are metal shields that are exposed to contact I attach them to the AC ground. This is for two reasons, first our electrical code requires all exposed metal parts to be either grounded or double insulated (hard to do). Second then the metal shields or cases can act as an EMI shield. A subset of this is if there is a completely internal shield. This can go either way to the AC ground or signal ground. It is hard to generalize here, try it both ways and use the one that works best. The method I use can be called a combination buss-star system as the busses are brought together like a star.
Now for why... Grounding has a number of functions and I won't go into all of them here. But three seem to me most important. You need to consider how power, signal and noise are handled by them. Anytime you send a current through a wire some noise is generated. The lower the impedance of the wire, the lower the noise voltage generated is going to be. The lower the current also the lower the noise. So what you want to accomplish is have minimal current (like power) flowing though grounds that connect signal components. Second you want to avoid alternate paths through the ground circuits. This is called a ground loop and will nearly always introduce hum and noise. The third function I already mentioned is personal safety. Any metal parts of an electronic device can get energized if the proper combination of faults occur. Perhaps not very likely, but being injured or killed is not something most of us choose to do. So if there is an internal fault, you want to make sure any voltages generated are conducted to the AC mains ground and not though your body.
Your other implied question on isolating the heater circuit has a different purpose. When you utilize a "totem pole" type configuration like the SRPP I used, the middle cathode is at about half the B+ voltage applied to the top anode. This voltage can exceed the heater to cathode rating for the tube. It can happen in steady state or during warm up as both sections might not warm up equally quickly. A common way to avoid this is to not ground the heater circuit and apply a reference voltage to it that is about 1/3 the value of the B+ on the upper anode. Then neither tube section will be in danger. There are some limitations to this method. Primarily it places a limit on the B+ that can be used. If you go to high (say over 350 volts) there is no good and safe value that will protect the tube under all situations. Fortunately in the designs I use there is little value in going over 300 v and often (like in the Forewatt) 200-225 is a good value to accomplish what is desired. All this said, many spec sheets on tubes give H-C ratings of up to 200 volts. I used to believe that until I smoked a few. Now I use the much more conservative ratings for the "worst" members of any given tube type which is generally 100 volts. There is another benefit to this method, usually the noise level is reduced slightly as it provides a bleed off path for wandering electrons emitted from the cathode that don't end up on the anodes.
I know the above is not a complete discussion of the issue, but I hope it helps a bit. Sorry for the length of the response.
Good listening
Bruce