When my husband proposed, he picked out a diamond and put it in a plain setting.  After I said yes, he took me back to the shop to pick out the setting/ring.  He said that, if I didn't find anything I liked, he could return everything and go elsewhere, but I told him, "if I can't find anything acceptable here, you need to throw me back."

I wouldn't care what kind of diamond it was.  I'm practical and would probably choose the lab grown one if it looks nice and is cheaper, but hopefully you know how your girl thinks.  Some girls care about brand and doing it the old fashioned way.  Some girls are more practical.