Check out this post for the allowed foods list that the forum follows:
I did phase 1 with brown rice and it only set me back because of sugar/starch content. However, during phase 2 the rice is not affecting me very much, so I would save any rice consumption for phase 2 personally.
During phase 2, I feel that the following types of rice would be best when compared to brown or white rice:
If you want a good alternative for phase 1, I recommend buckwheat.