This answer will vary from kid to kid, but typically they should be able to independently use a water bottle around age 3.  Most water bottles do not have small parts, but if they are tipped upside down they may leak, or they may involve buttons and latches that are tricky for younger kids to navigate on their own.  If a child can drink out of a straw, starting younger might make sense.  But we anticipate that by age 3 a child can independently most of the water bottles on this list.