If you can afford the bucks, a new bike would be a strong psychological boost/reward to yourself for your fitness effort. And if it results in more time with your daughter...that's a double score. While you could get more value for your dollars in a used bike, you would also be taking on more risk in that your ability to figure out your needs and fit would be all on you.
I have just moved on from a Trek 7.4 fx, which has good components that shifted well, and with a triple chain ring can climb almost any hill. My view is that a good local bike shop (ask around), would be the place for you. And if are willing to turn a wrench/allen key and get your hands a little greasy, start the learning process on bike mechanics and fit. All this will tie you in more to a good cardio activity....that is (gasp) fun.
Angie