Do I need an headphone amp?

Agree with Yidimsum. He is corrrect. (See my Portable System here on Audiogon).

Grados are efficient and can generally be driven straight out of a headphone jack of a receiver pretty nicely (32 ohms). The Sennheiser 580/600s are really inefficient at 300 ohms and a headamp helps a lot.

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.