I second basic judo as a great start that will translate right on to anything else. There is a short list of techniques and by the time you have those down, you will know if you want to change styles.
If you are not interested in competition, no competitive school is going to feel right. Just like competitive need people who feel there is something intrinsic that is missing, but they haven't put their finger on it.
Watch a competition. If you really like it, it is possible ...
If it's ok, but you wouldn't be into it or feel "not ready", that's the other answer too. I have shown youtube to people who start smiling real big because that was it ~
Karate has to be the next in line for a see-able completion and technique set? Enjoy finding out!
"The perfect way to do, is to be" ~ Lao Tzu