Phil/Lyman,
If you are including team photos and studio CdVs and cabinets, then Anson's (professional) rookie card would be either the 1871 Forest Citys CdV or the 1874 Suddards & Fennemore cabinet. Here is a link to the 1874 card, as it appeared on the Heritage website:
http://sports.ha.com/c/item.zx?saleNo=7028&lotNo=81174.
For Cartwright, ignoring dags and ambros, there are 1860s CdVs of him. And for Chadwick, the c. 1864 Resolutes CdV predates the 1870's cabinet on your list.
EDITED to add that for Anson he is also depicted on an 1872 Philadephia trade card.