Welcome to the forum EJ!
I haven't tried the EZ piano series, or Alfred's for that matter... so no idea. I did have some very old pop music in weird, big-note notation that I brought in to my teacher at one point, and he didn't like it at all...
If you like pop, you might try looking at the book "How To Play From A Fake Book" by Michael Esterowitz. I haven't had time to work through the whole thing, but it looks like a pretty good, clear explanation of what to do to play fake book (alot of pop and jazz) stuff and has some songs in the back to practice with, though nothing terribly exciting
(In case you're not familiar with it - fake books give you the melody and the chord symbols, you improvise the accompaniment.)
If you're looking for more classical, once you get a bit further along you might take a look at "Essential Keyboard Repertoire" series. These are short easy classical pieces that have NOT been "simplified". I've enjoyed working through alot of these pieces.
Billy Joel has a 2-volume set of his sheetmusic out there. The books are huge, and completely written out (not fake books). I find them very challenging though and haven't looked at them in awhile!
Welcome again, and happy new year!