Okay...I have an older son who had very specific reading requirements as an early reader (read aloud books I could pick and he listened and read silently along with me as we sat together but independent books he had rules about at the beginning)...
Nate the Great series (and the author has another series about his cousin too)
Mercy Watson books (Kate Dicamillo)
Amelia Bedilia
Then I moved him to Time Warp Trio, ABC Mysteries and on...but getting past the I NEED illustrations was pretty hard...I was patient and just did a lot of good lit during read aloud. Soon he took off and there was no stopping him. I think letting him have his illustrations until he was complaining and then explaining to him that if he wanted harder books he had to give up the illustrations rule...finally once the level of the books started being insulting he finally budged.