There seem to be a lot of opinions on how to handle grounding. and some work better than others. I have built a lot of gear, both solid state and tube, and I have usually found that the "star" ground system usually works best. In other words, ALL grounds eventually go to one point back at the power supply. With tube circuitry, running a heavy buss wire above the tube sockets that all signal grounds go to and returning that to the common ground point works well and adds a degree of "neatness" to the design. Power grounds have their own buss for bypass capacitors, again returning to the common ground point at the power supply. Sometimes with shields, one end would be grounded and the other end "RF" grounded by means of a .001mfd capacitor, so as to not have circulating currents through the shield. Another school of thought was the "brute force" shielding method, used by some, where the shield would be tack soldered the entire length to the chassis. With equipment that has both analog and digital circuitry, the grounds need to be seperate, and again only connect together back at the power supply. With PC boards, using double sided boards and leaving the top copper as ground usually eliminates the need for seperate grounds for audio and power in all but the most critical of low level circuitry. I'm being extra cautious here, because sometimes it just doesn't matter.
Which end of a shield to ground? I usually "telescope" the shield from the input, or grid, in the case of tubes. But doesn't that add capacitance to the input and shunt some of the signal to ground, cause wierd poles and zeros, etc?? Yes, but usually it's not a problem at the frequencies we're dealing with and the short distances involved. Some equipment will tie the other end of the shield to ground with a 10 Ohm resistor. Distance between conductors is the best insurance that you won't couple signals where you don't want them. This means tightly twisted AC filament supply wires snugly placed against the chassis and generally on the opposite side from where the components to the tube sockets are located. Avoid parallel runs and cross wires at a 90 degree angle to minimise coupling. A lot of thought on layout is needed before the soldering iron is turned on. There are lots of places to get information on good wiring practices, such as the ARRL handbook. That said, sometimes you will need several tries at wiring up a project, even when you follow the rules. Good luck!
