Hi Tereza,
In general, you want a cutoff value that is a bit greater than the greatest root height. If you use a cutoff value that is less than the greatest root height, the analysis may not detect certain aspects of the demographic history once you get further back in time than the cutoff value.
If you have a good idea beforehand of what such a value might be, you can enter it. Otherwise you can use the value that Beauti suggests. In either case, once you've completed the analysis, you should compare the cutoff value you used to the estimated root heights. If the greatest of the estimated root heights is substantially greater than the cutoff value, it would be a good idea to re-run the analysis using the greatest estimated root height as the cutoff value.
For the Skygrid reconstruction, it's advisable to use the trace which gives the greatest estimated root height. This will ensure that the plot depicts as much of the reconstructed demographic history as possible.
Hopefully that makes sense. Please let me know if I can help with anything else.