I have been practicing TM regularly for 38 years. This practice has given me a pervasive perspective on life. I know just a moment away is bliss. This sense of certain security is constantly in my awareness.

Zen meditation isn't really "the standard meditation", American culture just has an infatuation with Zen because the Beats and Hippies drew a lot of attention to the San Francisco Zen Center at the right time, while otherwise Buddhism and Hinduism have mostly stayed in immigrant communities. (I don't know enough about the Hare Krishnas to say anything either way.)

As others have pointed out, Zen is not "standard", but just one variety of meditation among many.

However, to answer your question: TM is focused on the internal repetition of a one-word Mantra, given to you by a teacher, and in that regard is not very different than mantra meditation you'd find in some Buddhist (Thai, Tibetan, Indian, Chinese) traditions.

(I should point out that I do Buddhist meditation myself, but I've had friends and family members do TM, and we've compared notes.)

If you are interested in meditation in general (and not TM specifically), there are a lot of meditation centers offering free (or nearly free) courses. I've never heard of a Buddhist center turning anyone away for lack of funds.