In the 1950s, an effort to increase the literacy rate resulted in the People's Republic of China (PRC) making the decision to simplify the written Chinese language making it easier for the general populace. Thus two distinct versions of written Chinese came into being - Traditional and Simplified Chinese. The Simplified Chinese writing system differs in two ways from the Traditional writing system: (1) a reduction of the number of strokes per character and (2) the reduction of the number of characters in common use (two different characters are now written with the same character).
With this in mind, I was leaning towards Simplified because it is commonly used in the mainland and is easier to read and write. My thought was that she could learn Traditional later on if she so desired. The decision was essentially made for me, however, when we discovered a Mandarin immersion school locally. The instructional materials they used were Simplified and we just stuck with it. In fact, a few of the resources I had purchased prior to enrolling her in the immersion class were Traditional (I later sold them).