"Zabrać się" is usually used in a fixed expression "zabrać się do pracy/roboty" which literally means "to get down to work".
"Pojechać" and "wybrać się" have very similar meaning; both verbs are applied with the purpose of expressing that we went somewhere.
Pojechałem nad morze/Wybrałem się nad morze - I went to the seaside.
"Dostać się" may mean, both literally and figuratively, to get somewhere overcoming some difficulties or obstacles.
Dostałem się na studia - I got into university.
Dostałem się na drugą stronę rzeki - I got across the river.
You will find this verb in a fixed expression "dostać się do niewoli" - to get captured, to become a prisoner of war.
I hope it helps a bit.