Watch the Barre One online guitar lesson by Brad Carlton from Chord Studies: CAGED Chords Vol. 2
This progression is a V - IV - I in the key of A. Our E chord is using a C form out of the CAGED system. You can choose to barre just the first three strings, or you can barre to the fifth string and use that first finger as a guide finger when moving to the D. You'll notice that when you move to the A chord you'll roll your third finger from a barre over to the fifth string, and utilize the E form out of CAGED system.