At the input to the tube (grid), the value is not terribly critical. I have used 10 kOhm as grid-stoppers on preamps, for instance, and it really doesn't effect the signal much because there is theoretically zero current flowing through it. In reality, there may be a tiny amount of current, but this is usually so small as to be negligible.
Do an internet search on "grid leak bias" to see how a tiny amount of grid current has been used in past designs.
The purpose of the grid-stopper is usually to damp any tiny oscillations which may occur due to the small amount of inter-electrode capacitance between the grid and another tube element. As a general rule, this is more critical in RF applications, but it is certainly not limited to them. In an audio circuit, such oscillations may do as little as contributing a "harshness" to the sound; in extreme cases, such an oscillation may end up being amplified by subsequent stages to the point of radiating in inconvenient ways or even causing "phantom" problems such as over-heating.
Of course, the only way to potentially "see" if that is happening is with a fast oscilloscope and some luck; just the act of attaching the scope probe at a certain point may disrupt an oscillation, making it a difficult critter to spot.
Conventional wisdom suggests that a resistance right at the grid can minimize the possibility of an oscillation being set up in the first place. The grid, of course, is inside the tube where we can't get at it, so we do the next best thing by attaching a resistance as close to tube-socket connection for the grid as we can. Because even a straight wire has some miniscule amount of inductance which might encourage the oscillation rather than damp it, it is usually recommended that the resistor be attached with as little lead between the socket and the body of the resistor as practical.
As far as the construction of the resistor is concerned, film-type resistors are usually made by etching away some resistive film until the desired value is achieved. As a rule, this ends up leaving a little spiral pattern of resistive film like a little coil, which may become a tiny inductance in its own right.
So conventional wisdom, again, says that a plain old carbon-comp resistor has less of a chance of being inductive than a film type, a wire-wound, etc. Certainly the carbon comp is readily available and cheap.
Now, the caveat: In any given instance, none of this may matter at all. Your circuit may not be oscillating, if it is it may not be causing any particular undesirable effects, or one tube might oscillate while another doesn't. Or, maybe a dirty tube pin or socket is enough of a grid-stopper, or maybe it's not.
The idea of including a grid-stopper is that it is cheap insurance. An extra carbon-comp is pennies against chasing a phantom oscillation, so it is a good design ideal to include it even if the chance that an oscillation will occur is slim.
And, yes, Virginia, any old resistor you happen to have lying around may serve the purpose. In this case, the odds are in favor of the least inductance you can introduce, so you look for something as inductance-free as possible.
There are a few choices, but, again the carbon comp is readily available and inexpensive. And, in this application the effect on the sound is pretty negligible no matter what you use, so that's not much of an issue.
So, if you're selling a kit, and the goal is to pick the better part for an intended purpose, when you find the one that meets your technical criteria AND it happens to be inexpensive and readily available, you've got your part! Especially when there isn't another type that is "better" in any objective or subjective way.
