I use 2, 3, 4 quite a lot and it makes for a simple change to the E chord as you describe because your index finger can stay in position behind the fretted notes when playing the A chord.
I also use 1, 2, 3.
And I also use 2, 1, 3.
And I also use mine-barre with index.
And it all depends on the song I'm olaying, the previous chord, thenext chord and whether I need to play any embellishments to the A chord (such as sus2 or sus4).
Long term you will want to learn more than one way of playing it.
In the very beginning, just to get you started, learn no more than one or two ways.
Keep your 2, 3, 4 and persevere with 2, 1, 3.