Do you get to play through all 3 storylines in FF6 ?

So I've just gotten FF6 on the PS Vita and oh boy! What a blast! I'm so excited to play through all the titles.

Anyway, I'm now at the part where SABIN gets thrown out of the raft and you have to choose between 3 storylines to continue. Will my choice be exclusive, or do I get to play all the storylines anyway?

Thanks