Normally you would want your character in T pose, or if you are using Rigify, create the character in typical Rigify, “arms half raised” pose. This is better because you do not distort the shoulders/upper arms as much when you raise them fully. If you look at how MakeHuman builds characters (just Internet search this), you will see the typical Rigify pose. Make sure you apply any scales/rotations/locations you have on the mesh and armature in Object Mode by using CTRL+A => “Rotation and Scale” then repeat for location. It is OK to scale a rig to fit a mesh, but you must apply the scale to the armature in Object Mode before you parent the mesh to it.
Rigging for a game is not something I am familiar with - you might like to ask this question in the Games forum as well.
PS. Welcome to BA!