Does either piece of equipment have a headphone jack? If yes, then I would suggest trying whichever headphones you like with the headphone jack first. If no, then you will need to feed a headphone amp from the tape monitor circuit.
I would suggest picking the headphones first as some headphones require an amp to sound their best while others will sound fine from a headphone jack. Also, not every headphone jack is a piece of junk as headphone amp manufacturers would lead you to believe. Headphones are a very personal choice, as not only sound quality, but comfort matters. If you do decide you need a headphone amp, I would suggest searching the forums at headwize.com and head-fi.org for more info.
I would suggest picking the headphones first as some headphones require an amp to sound their best while others will sound fine from a headphone jack. Also, not every headphone jack is a piece of junk as headphone amp manufacturers would lead you to believe. Headphones are a very personal choice, as not only sound quality, but comfort matters. If you do decide you need a headphone amp, I would suggest searching the forums at headwize.com and head-fi.org for more info.