If you mean the odd-ball paradigm of ERP (P-300), we use a response time of 1000 milliseconds to 500 milliseconds between stimuli. For most patients with 1000 milliseconds is sufficient.
But depending on the software you use can lengthen the reaction time all you want.
No problem with a longer response time (3000 milliseconds). You have to know what you want to study. You also set the parameters that allow you to get the optimal results.
The paradigm go / nogo usually does not require much time to respond. But it depends on the design of the protocol you want to do.
In designing any ERP experiment, you have three primary considerations:
1) The total length of the experiment
2) The number of stimuli to present (and responses to collect) per condition to get stable averages
3) The duration of each stimulus and response window to make the task doable
If you assume that the total length of the experiment is fixed, then the main balance is between the number of stimuli to present and the duration of each stimulus-response window. For example, let's assume an experiment that's 40 minutes long with 4 separate conditions of trials, or 10 minutes of stimulus-response window time total per condition.
Thus, if your primary components of interest are large (e.g., the P3b or LPP), or have a large signal-to-noise ratio, then you can have very long stimulus presentations and response windows. This can allow you to collect other psychophysiological data (like skin conductance) that has long onset, response, and reset times. If you need 20 trials in the experiment described above to get an acceptable average per condition, that means each stimulus-response combined time could be as long as 30 seconds.
However, if you have small components (e.g., auditory brainstem responses), you may need thousands of trials to get a usable ERP. Consequently, your stimuli will have to be short, and you may not have much room for any sort of response at all. In the experiment described above, if you need 1000 trials per condition, you would have a maximum of 600 ms for a stimulus-response combination, which is likely barely enough time for more than a simple reaction time measure to be collected validly.
For a Go/Nogo paradigm, you may want around 100 trials per condition (and ideally, the more the better). So in the experiment described above, let's assume the 4 conditions are Go-easy, Go-hard, Nogo-easy, Nogo-hard. That means in each condition, you could have a stimulus presentation-response window combination lasting up to 6 s per trial. You might choose to have the stimulus on for only 500 ms and allow a response window for the whole 6000 ms, or you may decide to do something different.
At that point, you may need to tweak the durations of the stimuli to make them appropriately easy or difficult for your participants. You might want the "easy" conditions to have stimuli last 2000 or 3000 ms, whereas the "hard" conditions to have stimuli lasting only 500 ms. Or in both types of conditions, the total stimulus duration might be 2000 ms, but in the "easy" condition the stimulus is unmasked, whereas in the "hard" condition it's presented for 350 ms then backward masked for 1650 ms. However, if you find that participants are committing too many errors with short stimulus durations (or too few with long duration), you might tweak the durations to give you the desired number of errors.
Hope this helps you think about future paradigm design!