get started with X - begin with X - start with X - make X be the first thing in a series.
Let's get started with a discussion of the basic principles. (As a way of beginning, let's discuss the basic principles first.)
-- There are a lot of things to do; we need to go shopping, prepare the sandwiches, pack the lunches, and get gas.
-- I think we should get started with the shopping. (We should make shopping the first thing we do.)
-- Why not start with getting the gas? (Why not get gas first?)
-- I've got enough gas to get to the market and back, so we don't have to start with getting gas.
This is the first time our group has met, and many of you don't know
each other, so I think we should get started with introductions. (Members of the group will introduce themselves to the others before anything else is done.)
_______
get started on X - get started working on X - begin to do work to accomplish X
We only have a few hours to fix the car, so let's get started on it. (Let's set ourselves to the work of accomplishing the task.)
-- Come and eat! It's time to eat!
-- Bad timing! I just got started on this letter. (I was starting to do work to accomplish the writing of the letter.)
Just as Henry got started on the assembly of his new bike, he discovered that a piece was missing. (Henry was at the beginning of working on the task of assembling the bike when he made the discovery.)
CJ