Basically with a minivan you are the same as a car in terms of rack types. I'm not an expert, but can tell you my experiences.

You have the standard car rack that goes on back. This is what I currently have. I have the Saris Bones rack which I was told was the best rack of this type and I haven't ever seen a better quality one.

Antoher option are the roof mount racks. These are supposed to be good, but it seems to me it would be too much trouble loading bikes that high up.

Third option (and best quality) are the hitch racks. You must get a hitch put on vehicle and then racks use the hitches. This is what I'm currently in the market for (just bought a new SUV) and started my own thread about. These are also the most expensive.

So.....I'd say if you want to spend more for the quality, get a hitch and a hitch rack (price of hitch + $150-300). If you want normal (like most people), get a Saris Bones car rack that will work on your van ($80-120).