I prefer to use my index finger on 2, and then bar the 444 bit with my ring finger.
Getting to E from other chords is what you should practice. I found it useful to practice going from E to the chords it is commonly found with in various songs (3 chord tricks such as E, A, B7). Also, look for songs that use E with other chords
for instance, in the song Hotel California we have an A, E, G combination
[Bm]On a dark desert highway, [F#]cool wind in my hair
[A]Warm smell of colitas [E]rising up through the air
[G]Up ahead in the distance, [D]I saw a shimmering light
[Em]My head grew heavy and my sight grew dim
[F#]I had to stop for the night
Good luck and good practicing