The spine of an arrow is the term used to describe its relative stiffness. An arrow needs to be able to flex when shot, since there is considerable energy being imparted to the shaft very suddenly. If you get a chance to see a slow motion video of an arrow being shot, you will see that it flexes or oscillates back and forth numerous times before it finally stabilizes.
Some of the things already mentioned are rules of thumb rather than absolutes. For example, 55/75 may generally be appropriate when shot from bows with poundages in that range. However, other factors will enter into the equation, such as how long the arrows are. A longer arrow will have weaker spine characteristics than the same arrow cut shorter. Also, the way the system works is that 400-rated shafts are, indeed, stiffer than 500's.
As for arrow weight, another rule of thumb is that you should generally not shoot an arrow that is lighter than 5 grains per pound of draw weight (too hard on the bow). 6 or 7 is fine and some shooters prefer heavier than that, especially for hunting. Bear in mind that a heavier arrow will have a slower velocity than a lighter one, and therefore a greater arc in its trajectory.
Beman ICS Hunters have been around for a long time and they're a perfectly adequate arrow. However, more advances have been made since their inception and there's lots of other good arrows out there. So have a good look around and you may find many that you would like.
BTW, it takes a lot of practice to be consistent at 50 yards, perfect bow/arrow combination or not. Just make sure you discover your own realistic limits and stick to them, especially for hunting.