A.B.
I would opt for a brand that has a low or, better yet, NO VOC content. No, paint fumes are not good for anyone to breathe. They off-gas for a long time.
Lowes carries Olympic and we loved it....almost NO fumes. Home Depot used to carry Fresh Aire, a no VOC paint that we used in the nursery. They are both awesome.
There are just so many toxins everywhere that we think it's worth avoiding them whenever possible. In this case, it's very possible.