You can do anything in all software.
Max is more of an architecture tool, it's like taking Maya and a cad software. People use it to make interiors, buildings, and neat hardsurface vehicles. Making characters is no problem, but you'd save time in Maya. It's more about architectural visualization rather than squishy organic modeling.
Maya is excellent for character development and animation and mainly game development as popular choice, there's a lot of tutorials, and it allows add-ons, and there's a lot. It's made use of
Arnold renderer in the recent 2017 version, and I love it, even with its quirky fallbacks. Importantly, it's making strides to directly connect its exportation options with Unity and Unreal, it's really easy to go back and forth between the two. However you will rely on secondary software to texture your models'n things. Software like Mudbox, Substance Painter, Zbrush, and hell, Blender has excellent painting services.
Blender is reliable, and it has everything you need, plus a caring community that supports it with many add-ons. Blender can do everything without switching windows, you can paint a character with both freehand, and procedural texturing. +10