Help! Question about guns!

[LochnarITB]

Wow, damage is a huge question. Billions of dollars go into researching such things so I doubt you'll get any simple answer. However, you are correct in that speed is more important than size (caliber). Speed is developed by the pressure generated by burning gun powder (as I'm sure you know) so the casing, which holds the powder as it burns and clamps the bullet in until the pressure is high enough to push the bullet out, is far more important to the result. Look up a .22 caliber and a .223 caliber. The caliber is similar enough that any real engineer would say "close enough to be the same" but look at the casings and the energy developed along with the applications they are each used for.

You also seem to be missing another complicated class of gun, the shotgun. They are measured in gauge and also vary widely based on the load, consisting of different amounts of powder and projectile (slug or BBs).

A couple things to start with would be these pieces about energies, muzzle energy and an energy calculator. Even energies aren't the answer because the energies have to be delivered and that varies with the construction of the projectile (hollow point, copper jacketed, etc.).

Have fun.