The first thing one should establish with a horse is forward movement, usually in a round pen, with person in middle directing it, as well as directing the horse's reversal of direction. I think that every neophyte should learn to effectively direct a horse from the ground first. Parelli Seven Games (7 games that horses play with each other, & the human should be able to play, too) is foundational, imo. Other teachers/programs don't call it the 7 Games, but they do them nevertheless. Jay O'Jay also has a good colt-starting video which shows you the first step of establishing forward movement very clearly.
All of the skill which you acquire with groundwork will transfer to your saddle time.