Give us links to school websites that you find.
Also, go watch a class and see if that is what you want to learn.
There are other things to watch for.
Kids wearing black belts will indicate no standards. Also, look at the higher ranks and see how they move? Do they all move the same when doing basics? If not, maybe there is no consistency in the teaching - no correction of mistakes - in other words poor teaching with no standards.
Watch how the teacher runs a class. Is he just standing there counting off while students punch and kick? Or is he making corrections and explaining details.
Karate and Tae Kwon Do are largely generic terms. Many TKD schools, and others, call what they do "karate" for marketing purposes. It's easier than trying to explain that "it's similar to karate".
What ever you do - NEVER SIGN A CONTRACT. My experience is that legit teachers do not have contracts. They may give you a discount for paying for several months at a time. But DO NOT sign anything long term or for a "black belt course".
Ask a lot questions, come back here and be careful.