Wild rice has a slowly lower glycemic index and better macronutrient breakdown then the other two but they are all extremely similar. Picking between one or the other is kind of nit picking.
Wild rice contains slightly more protein, zinc, and potassium than brown or white rice. It is also way more expensive. Kind of a small benefit for a large increase in cost. I personally just stick with brown rice but if you got some extra money to spend, wild rice is slightly superior.
Wild rice is the best option, followed by brown rice, followed by white rice.