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)