I understand the urge to tackle new stuff. But if you're not quite through with PH 1 yet, you're missing a few key skills that all of the above suggestions are going to require of you. Namely:
- Playing eighth notes and dotted quarter notes against left hand patterns
- Minor chords and 7th chords
- Alternating basses
- Notes in new keys and in higher positions on the staff
So my first recommendation would be to try to plow on through Book One and, when you're done, just
move right on to Book Two.
Book Two actually starts out with a couple of "review" tunes at the same level as Book One, and then (in the well-paced style PH is known for) very gradually introduces the above topics. So it's not much of a leap at all, and you should be perfectly fine without any supplemental material.
That said, PH
does have extra material at the Book One level, although it's not always easy to find/get:
Palmer Hughes "Recital Book" Book One -- Similar songs to those found in the main method book, only a bit longer. That is, suitable for a recital. Each piece in the book indicates the song in the main book that you should be able to play to before tackling that one.
If you go here and click on the preview PDF, you'll get half of one of the pieces to try out for free! (There are also recital books for the next couple of main method books, and they're worth getting too, IMHO.)
Palmer Hughes Books 1A and 1B -- Back in the day, in addition to the regular series of method books, they made sort of a "extended edition" version of the first few books, that takes things at a more, um,
leisurely pace. If you look on the back of Book One, at the bottom, there's an advertisement/explanation of how those A/B books work. Every piece that's in the regular Book One is also found in either 1A or 1B, but there are also a lot of
extra pieces included at the appropriate level. Not sure if they're still being published--you might have to hit eBay, etc.
Once you finish Book Two, you'll be well-equipped to branch out to supplemental beginner-to-early-intermediate material.