To identify what output impedance a part of a system should have you need to know a lot of thing, some of them you have not specified.
If you don't have the static losses of pull-up resistors, generally you try to get a low output impedance, since this gives drive strength. Capacitance on wires or PCB traces will make your rise times slower the higher your output impedance.
That said, there are reasons to not go for the lowest possible output impedance, or the highest possible input impedance. One such reason, which is very common, is matched impedance with the medium.
For example, if you would be using a specific cable between this block and the next and that is of 100Ohm characteristic impedance, then if you have a long way to go (where what is long depends on the sharpness of the flanks and the signal frequency) you will want to match that impedance at least on one side, possibly on both, to be able to transmit without reflections.
But, basically, the checklist I most commonly run through is:
- Will I be transmitting across a distance of 1/4th the wavelength of my signal or more? --> No = Characteristic matching is much less of an issue. Be aware that for square waves, the wavelength is much shorter, since the sharp switching edges introduce higher order harmonics. How many harmonics you need to stay "reflectionless" depends on how much your signal is allowed to distort.
- Yes to the previous one: What is my medium and can I estimate the characteristic impedance of it and can I find a scheme to make my design compatible with that without any reflections.
- If not trying to match: Will my output impedance notice the device or wires that I attach to my module? For this, you need to think of capacitance on the wires and the resulting rise and fall time. But also the input impedance of the next thing. If the next thing is 1GOhm and it stays 1GOhm dynamically, that's a none-issue for anything lower than 50kOhm output, since that's only an 5% error, which should be allowed in any signal.
- Resulting from the previous one: Is my input impedance specified in a DC situation, or for transient situations? Many inputs specify a DC input Impedance and a pin input capacitance, you then need to judge whether that capacitance influences your rise times, since the capacitance effectively makes your input impedance different for high frequency signals or fast changing ones like a square wave.
- Will a specific output impedance damage anything due to over-driving, high transient currents, or too high power usage. This is one of the few ones, other than impedance matching, that may create a lower bound. Again coming back to the input capacitance, if that is a MOSFET input and the MOSFET used is tiny and fragile, it may not be happy about you having a 100 Ohm output impedance directly into its gate, as the gate capacitance (input capacitance) may spike a current not supported by the device. It's extremely unlikely to be a problem though, and if it could be the datasheet will (should!) always indicate a required input resistor on that pin. Otherwise a low value resistor in the pull-up of your specific schematic may cause your comparator to not go far enough to 0V any more, but that's down to your own specs.
And I probably forget a few here that I either instinctively judge in the process of any of the other steps, or that are more specific to certain designs I have not made in the last 5 years. Apart from that, my apologies that I couldn't write this as a simple flow chart with side-notes.