Say "I should get going" when you're ready to leave somewhere:
Well, I guess I should get going.
This sounds softer and friendlier than "I should go".
"Get ___ing" means to start doing something. It's used in casual speech. But this structure that can't be used for just any verb. Only a few good examples come to mind:
- get going
- get moving (often used when leaving your house)
- get the ball rolling (to start a process or a project)