This repository contains a .blend file of two prototyping rigged meshes that should be importable in Unity and Unreal, with a few sample animations.
I did not use Riggify for this because it provides a rig that is not directly usable in your usual game engine (though it can be converted with the help of an addon)
The mesh is a modified version of the male and female Blender demo base mesh
Note that I am not a professional rigger/animator, so this rig can probably be improved in ways I don't know about. Feedback is appreciated!