I think the best way is the same way we learn most things, that is by mastering a multitude of small achievable steps. However it makes sense to have a plan where each step builds on what has been learned in an organised and structured way.
I have found the best way to teach beginners of all ages is to use simple songs in 3/4 time using an oom-pah-pah bass. This pattern can have students sounding good quite quickly and 3/4 gives them a little more time to think about what they are doing and what comes next. It is the first pattern I use in my lead sheet method books, Playing with Chords.
This is the suggested pattern for the first chord C.
The low G (the fifth) in the second bar makes the pattern slightly more difficult but it is worth persevering with because it sounds so much better. Repeating the root in every bar quickly becomes monotonous and boring.
The course begins with the two chords built on the tonic, C and the dominant, G. (The 1 chord and the 5 chord). There are thousands of songs that only have these two chords. You would expect the G chord to mimic the C chord, like this.
However, there is a problem. The notes are high on the keyboard and will often be playing the same notes the right hand needs to play, especially when harmony notes under the melody are introduced.
Fortunately there is an excellent solution to this problem. Instead of a G chord I skip straight to a G7 chord using this pattern.
This not only ameliorates the problem of the overlapping hands it also means the hand position for the C and the G7 chords are very close which is desirable. There is a strong rhythm component and most importantly, it sounds great. Even when the right hand is only playing a single melody note this pattern enables beginners to produce a satisfying sound. Playing with Chords includes songs with these two chords to practice, plus there are many songs that could be added.
The third chord to introduce, of course, is F. Then our student will know the three primary chords in the key of C. F has the same problem as G, it is too high and will cause problems with both hands wanting to play the same notes. F7 is not an option in this case. The solution is a little complicated but the student has to learn to improvise, solve problems and adapt.
The suggested solution is to alternate a low root and fifth on the first beat and play a chord on beats two and three as high as practical without clashing with the right hand.