I suppose a skylight is out of the question?
The best quality light yet is from the T-5 fluorescents.... and it's much less likely to create harsh shadows than any HID. Being a batters' cage, I would place a sheet of plexiglass in front of the fixture. I'd also mount the fixtures so they could move if hit.
(I say "plexiglass", an acrylic, as Lexan will be yellowed and made brittle by the UV from the fluorescent bulbs.)