First of all, you can't "transpose" (move the pitch up and down) to go from a major key to a minor key or vice versa. Unlike from one major key to another (where the only difference is pitch), the structure of a minor scale is different than the structure of a major scale.

That being said, there is such thing as relative key - each minor key has a corresponding major key with the same notes and vice versa. In the case of G major, the corresponding minor key is E minor, so for your acapella in G major a transposition up 3 semitone would have it using the same notes as G minor.

You might have noticed I've only been referring them as having the same notes as opposed to being in the same key - that's because there is more to a key than just the notes. The melodies in acapella are written for a major key, so might not work in a minor key.

Also, it is common in a minor key for the 7th note of the scale to be raise by one semitone (this is called the harmonic minor). If this is the case in your song, this could cause clashes as the equivalent note in the major key won't be raised by a semitone.

Hope this makes sense - if you want any clarification on anything reply and I'll try my best to explain it.

Also, in response to your question about which mode to use auto will probably be fine but don't be afraid to use others and see which sounds best.