Not sure what the actual comparison is in your question. If it is shelf life that you are talking about--white rice is going to last longer than brown rice. Instant rice is partially cooked and will not have quite as long a shelf life. Long grain rice is not necessarily a different "animal"--it is often just a longer rice grain, although there are dozens of available rice types out there that I am aware of.
Of course, how you are going to store the rice, how you preserve it, in what conditions you'll store it, and what your intended use is for the rice also can come into play in determining what a better rice is.
That said--I am not an expert on rice, and I don't even care for most rice dishes personally. I do know that rice in general is the single most important food on the planet in terms of providing basic caloric nutrition. It's a valid, economical storage food, but to get maximum shelf life--you want to be sure you vacuum-pack white rice that is uncooked.