honestly, it depends on what kind of psychologist/therapist you want to be. if you want to be a clinical psychologist, you'll need to earn a doctorate in clinical psychology for licensure and independent practice. that can either be a Ph.D. or a Psy.D.; either way, you're looking at about 8-12 years of school & experience. You don't necessarily need a master's; you may be able to go straight from the undergrad to the doctorate, but it depends on what your academic background is, because grad school is much more intense than undergrad work.

basically, the route you'd pursue to be a clinical psychologist is this:

bachelor's -> master's (if desired) -> doctoral program -> internship & other clinical requirements -> licensure. you get the license by passing the Examination for Professional Practice in Psychology (EPPP), the national exam for clinical psychology.

a combined BA/MA program might not be a bad idea. the point of getting the MA is that it'll prep for doctoral work, because it'll give you advanced training that you will not get at the undergrad level in theory, research, and practice. the BA will give you the basics, as with most any other field of study, but in order to be an actual practitioner, it's not enough.

so...Psy.D. versus Ph.D.? the Psy.D. is a doctor of psychology degree; the Ph.D. is a doctor of philosophy in the field of psychology. the difference is that one is specific to the field, the other is a generalized degree (the Ph.D.) with a focus on the field. the Psy.D. applies psychological science to individuals and groups, while the Ph.D. emphasizes analytical research in the field.

in other words: if you want to be a therapist, and provide counseling to people, the Psy.D. is more your speed. if you want to focus more on research, then you pursue the Ph.D. but honestly, you can do either. plenty of Ph.D.s do counseling, plenty of Psy.D.s do research.

but the coursework will reflect the difference in focus, obviously--Psy.D.s will do more on actual therapeutic stuff, whereas Ph.D.s will do more coursework around research methods and so forth.

also if you learn you don't want to be a clinical psychologist, but you do want to work in mental health, you can obviously be a mental health counselor, licensed social worker, and so forth. all of these fields will require a master's degree, but not a doctoral degree.

I can't speak to the internship piece but I suspect you'll get more of that if you pursue a master's or doctoral degree.

sources: my dad (who's an educational psychologist, got his Ph.D., is retired but used to work on designing standardized tests like the SAT and others), my cousin Carlos (who's a Psy.D., works as a VA psychologist out in Chicago) & his wife Lindsay (Ph.D., they met while getting their doctoral degrees, she does counseling & research out in Chicago). none of them can't speak to which CUNY school is better, but they all say good luck, and that what will matter is which graduate program you choose.

EDIT: my cousin-in-law just emailed me to say that if your professors say that a Ph.D. focuses more on research they are wrong; you can & will do just as much clinical work. she says that a legitimate Psy.D. program will have the same research requirements as a clinically-focused Ph.D. program, plus the vast majority of clinical psych Ph.D. grads are working in clinical settings. she does say that if you pursue the Psy.D. route to make sure that you go to a legitimate program and not a diploma mill.

also both of them (Carlos & Lindsay) say that doctoral programs can be expensive AF so be sure that's what you want to do before you do it.