It's a difficult subject. My first book Tortoise George was Times Roman and I've have a few criticisms about it.
I had tried many fonts next to their associated illustrations and found that Times Roman looked the best. My justification in part being that Dr. Seuss used New Century Schoolbook which is very similar.
Since then I've been googling some more and found that if you ask 100 people you'll get 100 different answers. Ok, maybe 33 different answers. Some people like Times Roman, some people like Arial. The bigger question is whether to be serif or sans.
The one thing I don't want to do (currently) is to pay for a font. That may change of course.
Let me know what you think. Below is an illustration from the forthcoming "My Nana is from Neptune" - let me know which font you think works best - left or right - if if you think both suck, please feel free to suggest a font.