At the beginning stages of your journey towards learning to play guitar, your best approach would be to memorize the basic chord shapes (formations) of the chords you want to play. So you know that an A major chord requires you to fret the D G and B strings on the second fret. For now that is all you need to know to play an A chord.
You can build quite a large vocabulary of basic chords in standard tuning by simply memorizing how to play them and putting them into practice. For many years I accompanied my singing by playing songs I loved on guitar, without having any idea what actual notes I was playing. I just knew that to form an Em chord I would fret the A and D string on the second fret and play all six strings. And to play an A major chord ....... etc.
To take my point one step further, I did not even know that the strings I was fretting for an Em were the A and D string, all I needed to know was to fret the next to the fattest string and the one beside that one. The names of the strings or notes I was playing were irrelevant. I just knew that I was playing an Em chord - and that was all the information I needed at the time.
As you advance, if you plan to play with other musicians or experiment with alternate tunings, it will be helpful to start learning which notes you are playing in the chords. But in the beginning, it will suffice to know only what chord you are playing (the name of the chord ie. A minor, G major etc.) and how to finger the various voicings you want to use for each chord.
In other words, you can go a long way in your guitar playing, by learning to associate and memorize the various shapes and formations with the names of the chords you want to play. Then when you look at chord based lead sheets or sheet music with the chords written on top of the staff or above the lyrics, and you see that the chords are G, D and C - you will be able to play the song. You only need to know how to form the chords at first. Knowing which notes you are actually playing, can come later.
Trying to memorize every note at the beginner level, will IMHO - only impede the process of getting to a level where you are deriving enjoyment from playing songs you like. It will make learning the instrument more academic and less fun. So I would encourage you not to worry about memorizing individual notes at this stage, but instead memorize the formations and shapes for the chords.
As you learn the basic open or first position basic chords, you might want to begin to learn alternate voicings and barre chords. With barre chords that are based on the E string or A string, it is helpful to know the root note played on the bass string of the chord so you can easily find the correct fret to barre for a particular chord. Or you can just remember that an E shaped barre chord on the 5th fret is an A chord.
Good luck with your journey. Try to make it as much fun as you can in the beginning. As your passion for guitar and your desire to improve your skills builds, you can start learning more about the notes on the fretboard and how they fit in with the chords.