Here is an excellent presentation of the problem and solutions to it. http://www.kiwiukulele.co.nz/images/KUKEp20.pdf
Personally, I prefer using the alternate D AND the E using the same format as the alternate D. However, I’m not opposed to the traditional D as I used to be. You pretty much can ‘barre’ the top three strings and if your finger touches the bottom string then it pretty much just mutes the string anyway.
As far as the E is concerned. The alternate E is just so much easier than the traditional one. The fingering in the lower example on the chart may work fine for you though.
It is recommended that you know the different methods because sometimes one fits into a song better than another (based on what other chords are required and the order of those chords in the song).