Pink Piano
When I started teaching I went to my local music shop and looked through every piano beginners method book I could find - it took about 2 hours! I had a few ideas about things I was looking for and these were:
a) Step by step development

Starting from the strong fingers ie 1 2 3
c) Using right and left hand from the start
d) Not staying in middle C position for too long
e) Presentation suitable for the age group I was interested in
f) a personal thing for me - I wanted "english" terminology like crotchets rather than quarter notes
It was a very useful exercise as I discarded straight away many methods and homed in on the following:
For tiny beginners ie 6 and under - I don't take children this young but my friend does and uses "Ministeps"
For young beginners eg 6-8 Tunes for 10 fingers
Age 8 - 10 Piano Time (Pauline Hall)
For teenagers and adults - Classic Piano Course (Carol Barratt)
All of these have their own foibles and areas where there are gaps or they go too fast or whatever but you only find these out as you go along. For example in Piano Time around page 9 it suddenly leaps ahead and some people are left floundering. So now I introduce a second book as well either from the start or part way through which I use to reinforce the teaching in the main book or as a bit of extra practice when things get tough.
For example I use Me and My Piano to reinforce Tunes for 10 fingers - but I would never use Me and My piano on its own because it does all the fingers in the right hand first before starting on the left hand, and when you get the the end the pieces are suddenly really hard.
I have used Jibbidy F to reinforce with a child who is really struggling.
I reinforce Piano Time with Party Time, Roundabout or Piano Time Pieces depending upon the ability.
I reinforce Classic Piano Course with Classics to Moderns or Piano Time Pieces or even Piano Time.
For some reason I discarded the Chester course but I will go back and have a look at it to see if I missed something. I also didn't like the look of the Alfred stuff but it is very personal so you have to do what suits you. I would definitely do the choosing myself rather than let the children so it because they will do it purely on the pictures!!!
Once you actually get started with the teaching you will find out how suitable your choices were and don't be afraid to ask them to buy another book part way through the first one - you don't have to say it's because the one you chose doesn't seem to be working! If you say right at the start that you expect to supplement it with another one later then it is much easier to do this.
Hope this helps