To eat or not to eat - that is the question....
I know my daughter (and us too) loves the chance to meet characters whenever possible. She was scared of them the fist time she went (she was 6 at the time) but now (about 2 years later) she really loves them and usually takes every opportunity to meet them.
I think a character dining experience at the beginning of your trip, is a good way to get your child comfortable with them.
If money or time isn't a problem then I say do 1 every day. This can save you time in the parks as you won't have to stop as much to meet characters you already met. But you can take a lot more time eating at table service meals (plan on at least 1 - 1.5 hours per table service meal) plus the cost is high for most sit down meals - if you're on the dining plan then no worries.
We are going at the end of next week and have the dining plan and have booked 4 character meals. The food is usually good and it's always fun to meet the characters - I think that it helps to set Disney apart from the others parks. Where else can you have Pooh, Cinderella or Stitch come to your table to visit while you are eating? I also find they can be a very memorable experience - on a previous trip my daughter wouldn't stop talking to eat (too excited), so when Meeko (we ate at Liberty Tree)came by he saw this & actually fed her the desert she wouldn't eat! Very funny!
One more thing... character meals are also a convenient way of collecting photos and autographs of your fav characters w/o standing in line. For example you can eat at the storybook breakfast in Epcot to see most of the Princesses in one shot (except Cinderella - she is only at the Castle for breakfast) - this is great if your daughter is a fan of the Disney Princesses (unless she is a fan of Cinderella). We ate there last year (eating there again this trip) & met - Mulan, Aurora, Belle, Snow White & Jasmine.