When I was losing weight, moderation was key. It wasn't about cutting a single item out, it was about cutting the excesses out. A small bowl of rice or oatmeal, maybe potatoes was fine, 3 or 4 was not. When I tried to cut out specific things, I found it harder to stick with it.
It's also 50/50 exercise and diet for me. I found dieting to be almost ineffective when I wasn't exercising with it. I might have looked a little better, but I was just as unhealthy. 30 minutes a day is plenty, just get the blood flowing and stretch out well, you might find it to be extremely helpful if you aren't doing it already. It definitely was for me.