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I am learning and I have already seen three ways of playing A major chord.
The 2-3-4 and then 1-2-3 and then 2-1-3 (I found this one to be easy).
I am willing to do the hard miles and learn the right way which helps me later.
I do not want to learn something easy now and later on find that I have to re-learn how to play the chord so that I can switch easily between chords.
There is no right way! There may be a right way for you, or me, but there is no universal right way!
Several reasons why one may be better can be found.
Using M A P will suit people whose fingers are fatter. Those three take up the least space.
Using M I A moves the I out of the way - as Justin says. It also facilitates moving directly to Amaj7, which can follow A major.
Using M A P works best for me, due to being able to put I on 3rd string, 1st fret, where it won't make a scrap of difference, but is ready for the almost inevitable E chord that precedes or follows.
Those with very big fingers may favour M and A, where the fingers spread out over all three strings.
Some merely use one finger, in a sort of semi-barre, which covers all three, but raises enough to allow the top (thin) string to still sound.
So, as you can see, any - or probably a couple - of these will suit each person best, for reasons given. I find that a lot of players will have two versions they prefer, depending what the chord before or after was or will be. I expect my students to explore every possible fingering, and then they will decide which suits. I suggest you do likewise - with every chord shape you ever meet !
By the way - I=index, M=middle, A=ring, P=pinky. Those who also play piano call thumb '1', which can be confusing.
I think the two fingerings I use the most often are (D-G-B string order):
If I try to use three large fingers (1, 2 and 3), one of them ends up farther away from the fret which causes risk of fret buzz.
Different shapes/fingerings will often become more comfortable/natural with time.
Personally, I play it either as 1-1-1 (barre-like), 1-2-3, or 2-3-4. It kinda depends on what I'm playing whether I'll gravitate towards barre-like or the more "spelled-out" versions. Same thing with open D.
I find barre-like forms as the most effective ways to play transposable Gs and Ds, but I mean folks often just omit some notes to play them comfortably. I do this too sometimes and I think it sounds just fine. I can see the 2-3-4 form being useful as it's similar to the "spelled-out" transposable A (I do usually use a barre-like form for this one though).
If you have a guitar teacher, they may be more helpful in providing you with guidance for accelerated learning as they likely work with many new players.
From my experience, I prefer knowing a few different ways to play things. I often follow what's most comfortable/low-energy to play, but that can change depending on what I'm playing and the chord changes involved. The important things are to enjoy it, be challenged by it, and to not hurt yourself doing it. If I were to find myself hurting or straining ("the wrong way"), then I'd stop playing and think about those red flags.
The best way to play it with multiple fingers for ME is, as you describe, 2-1-3. Here’s why:
An A Major chord, in modern popular music, will most often be played as the I in the key of A, the IV in the key of E, or the V in the key of D. So this means it is most often moving to and from the Major chords D, E, G and B.
In any of these cases, 2-1-3 facilitates efficient movement from the A chord to both D and E chords, as the index finger never leaves the string. This provides an anchor/reference point that is easy to feel and not have to support visually, so it’s easier to switch chords without looking. Similarly, as mentioned previously, it also facilitates efficient movement of index finger down a half-step for an A-Maj 7th chord, or just lift it for dom 7th.
When the open G chord is played with pinky on high e string (which I find most advantageous for that chord,) having the pinky free on the A chord allows efficient movement to that G chord. The pinky is naturally positioned at the 3rd fret on the high e string, so you can just put it there and then move your ring and middle fingers to their positions on the E and A strings.
B Maj chord is a barre shape that none of the multi-finger arrangements listed really facilitate movement to. However B7 (dominant) can be played open, and its finger arrangement is also 2-1-3, just with finger 1 a fret lower, so it’s also fairly efficient to move between the A and B7 chords.
Besides moving between chords, 2-1-3 also keeps the pinky finger available for any number of augmentations of the A chord.
Additionally, barring the D-G-B strings at second fret with index finger (1-1-1,) whether the high e string gets muted or not, is also useful. It does facilitate easy movement to the B Maj barre chord, and also frees up a couple more fingers for augmentations. I play it this way in a lot of situations, but if I need the high e string to ring out cleanly, I’ll usually go with 2-1-3.
Hope that all makes sense and is helpful.
"There is no one correct way."
But...
I like to fret open A with 213 because it prepares me for a quick transition to D without moving the index finger, and to E with just moving it back one fret. This is useful for playing in D and A.
My second favorite is to barre those notes with my index finger, leaving me open fingers to play boogie-woogie sixths, like in blues or western swing. This is good for A or E. Come to think of it, this is likely what I use most often. I often end up with a muted high E, but I already have the E on the D string and, depending on need, a low E too make it A/E.
I've experimented with 324, which would allow you to quickly move up with a barred A-type chord without too much work. Normally, though, I would tend to a two-finger barre fingering for this purpose.
So, my preferred A fingering depends a lot on what I expect to play next and what open strings I might want.
All the answers offer good information but I like the one by wabisabied because it offers some logic behind the answer (even though I'd disagree with the actual statement it supports).
The fact is that every possible way to finger the chord serves a purpose. In choosing a fingering you need to satisfy a couple requirements: (1) does the fingering produce a good tone and (2) will it facilitate easy, optimal, movement from the chord to neighboring chords in the piece of music you are playing.
There are major problems with fingerings like (1, 2, 3) and (2, 3, 4) on the classical guitar in that these fingerings tend to force the E played on the second fret of the D string to be improperly fretted. Ideally, one should try and fret the note with the finger close to the fret that defines the boundary condition for a string "fixed" at two ends. It is a common misunderstanding that you can place your finger anywhere in the space between two frets to play the note defined by the higher numbered fret. This is not true. What happens when you finger the note too far back is you have a string that is free to slide on the fret that defines the note. This can cause severe buzzing and a weak sound with poor tone. This can happen on any guitar, electric or classical, but I find that the issue is very noticeable on the classical. The issue is exacerbated by the fact that the D string is wound which makes the buzzing more severe. In contrast the fingering (2, 1, 3) allows one to pinch the E on the D string right up to the fret. The A on the G string will be fretted slightly far back but more towards the center of the space between the frets.
With a little practice you might be able to correct the issue mentioned above using a fingering like (1, 2, 3) or (2, 3, 4) but there are other considerations. In moving from one chord to another you want the movement to be easy, smooth and, if you care about it as many classical guitarists do, avoids squeaking or scratching noises. You want to be able to release the strings (without completely opening the hand) and generate the new chord form quickly. As several answers point out this is facilitated by different fingerings for different progressions. A common movement is A --> E7, or I --> V7, and a common fingering for the E7 is (2, 1, 3) on frets (2, 1, 3) of the (E, G, B) strings. As you can see this is the same ordering of fingers as the (2, 1, 3) option for the A chord. So the movement allows you to keep finger 2 planted and 1 and 3 can simply slide back and forward by a fret. This is an optimal fingering for this movement. By the way, this implies that one might finger the same chord 2 or more ways in the same piece of music and we often do.
Other considerations are physiology, e.g. if your fingers are too large you may need to experiment with alternatives or find a way to get optimal movement and clean sound other ways. But the take away is that there is more than one "right way" to play all chords and the motive behind the choice is motivated by the two points made in the beginning of my answer (1) clean tone, and (2) optimal movement to other chords.
