Honestly, you can't get the staff these days can you.
I teach an eight year old using Hal Leonard, but it's not enough on its own. The tunes in that book are very simple and do what they set out to do. With this particular student, I use a book of Disney songs; he knows them and they are arranged simply so that beginners can sound good.
The Russ Shipton books are fine, if you know the songs, and I find that older students need to start playing something very early on. It doesn't matter what, so long as they know it and can get playing it. My suggestion is that you use the Russ Shipton books as much as you can, but don't necessarily make it your sole learning material - it's not hot on explaining theoretical points and concepts as I recall.
The reason we say "start slowly" is because whilst a simple song with three or four chords might not be too complicated to play well, if you're going to play something comlicated then you'll need to start slowly because ifyou can't play it slowly you'll never play it at full speed. Playing at speed does not produce poor technique, but poor technique will be magnified when trying to play at speed.
Also, somethings are not good to start with at speed - barre chords being the most obvious.