There are various reasons for sizing hooks this way and there is no industry standard, so a 1/0 hook from one company may vary in size from a 1/0 hook from another company. The size is supposed to be based on the gap between the shank and the point, but it is a relational number, compared to other hook sizes, not based on a measurement.
The smallest hook is a #32, the largest is a 20/0. The 20/0 would be suitable for great white sharks, the #32 for tiny gnat flies used to entice small trout. There is no size 0 hook.
Hook prices are somewhat based on hook size. You generally get a lot more small hooks in a pack than bigger hooks. For example, a #6 bream hook that I use for catching bluegill in my pond with floating fish food I buy in boxes of 100. For 6/0 worm hooks that I use in big worms like the Zoom Old Monster for bass fishing I usually buy a ten pack. Ten of the bigger hooks costs about the same as 100 of the smaller hooks.
You can get hooks in lots of sizes and styles from many manufacturers (compare prices) like Eagle Claw (compare prices), Gamakatsu, (compare prices) Owner, (compare prices)
There is no perfect size hook, even for one species of fish. For bass fishing I use hooks ranging from #1 to 6/0. For bluegill I use #6 hooks most of the time but drop down to #8 if most of the fish are smaller and go up to a #4 if the fish are really big and I want a stronger hook.
Try different sizes and styles of hooks to see what works best for you. Also try different manufacturers until you find the one you like best.