What We Found for E
The fret number can be viewed as the the 3 finger [the root on string 4] or the 2 finger [5th on string 5].
Memorize the names for these chords in each position.
And finally [or start with these - order of training is up to you], we get all the fingers moving together in blocks. When we train, a good practice is to alternate between arpeggios, finger flutters, & blocks. This is cross-training. Study your motion. Get comfortable. Find your picking pocket.
Another option for this key, in this position, is moving the F# to string 6 and the E to string 4, fret 2. This chord is based on an E form. It could be called Am/F# [Am chord with an F# in the bass].