At 3, there are not too many options. Gymnastics is great at that age because it works on flexibility, balance, and strength which will benefit any sport in the future. At 4-6, soccer is good to introduce because it works on footwork and conditioning. I don't recommend any of the skill sports at those early ages unless there is one that you know really well yourself. Pitch and catch with anything is enough. 7 on up, just see what she likes. They are usually different seasons, so you can try a few in a years time. Around 10, she needs to be settled into 1-2 of them.
