ask for Schwalbe Marathon Plus tires (+1 on skipping Slime). the Marathon Plus tires are pretty much the best tire for bomb-proof city riding. check the Commuter thread if you don't believe me.
super excellent that your kid likes the rides with you. i know it saved my sanity to be able to get outside in a healthy manner and still have my kid take a long nap (or play in a park, or both).