I know people love to pick on TaeKwon-Do here, but I'll have to put my $0.02 worth in here.
I had 27 years into TKD, 23 of them teaching it. I wasn't too terribly interested in promoting every time I had the chance so I ended up with a Samdan black belt in ITF style. For those of you who may not know much about TKD other than what you hear / read, ITF is the original style, blending Shotokan karate and TaeKyun. It has no relationship to the newer WTF (Olympic) style TKD. Just for reference, my textbook includes Nihanchi Shodan as a legitimate hyung / kata.
After a number of years in TKD I decided I needed to branch out. Forays into Shorin-Ryu, Ueichi-Ryu and Aikido broadened my horizons.
One thing I can tell you, to paraphrase the late, great Bruce Lee... "when I first started in martial arts, a punch was just a punch. After I learned for a while, a punch became something more. After I had spent a number of years in martial arts I found that a punch was just a punch." I found that there are only so many ways that the human body can move. TKD, JKD, Shotokan, Wu-Shu, Muy Thai... they all emphasize particular aspects but in the end they are all the same.
Now, grappling vs. striking arts are a whole 'nuther story. Despite what a number of people say, NOT all fights end up on the ground. BJJ is not the be-all, end-all of martial arts but some grappling skills are essential to a well rounded martial artist as are striking skills. Just as you don't want to JUST have a gun in your arsenal of skills you do not want to only have grappling / striking skills.
I guess what my long-winded post is saying is to find a good school and study whatever style it is until you are proficient. THEN branch out.