1.) The caliber is expressed in decimals of an inch, in most American originated calibers, or in millimeters for chamberings of European origin. The caliber is the diameter of the bullet, and there are often many chamberings that will use the same size bullet, but may vary radically in power.
A .45 is roughly 45 one hundredths of an inch (45/100). A 9mm, if expressed in 'American' terms would be a .355 caliber. However, manufacturers have confused the issue through the years by such marketing decisions as calling certain .357 diameter chamberings as .38 caliber, or by calling certain 9mm chamberings .380 caliber, etc. Quite a bit of reading will be necessary for you to grasp all the little variations, but this should give you the general idea. Just don't assume that caliber tells the whole story about the power of a gun.
2.) Since you have already fired a .45 and liked it, there are hundreds of possibilities for you. You already know that a .22 is great for practice, so you may want one of them so that you can afford to shoot more often. You should try a good semi-auto chambered for 9mm (aka Luger, Parbellum, 9x19, etc.). It is a chambering that will allow you to shoot low-power practice ammo, but can also accept high-powered self-defense ammo - a great chambering that is still popular after about a century (like the .45 ACP).
In that same vein, you owe it to yourself to try a revolver chambered for .357 magnum, because it is capable of shooting very powerful magnum loads, or very comfortable .38 special loads. It is a great all around shooter, and nothing outdoes the .357 magnum for self defense purposes.
I would avoid .380 for anything except a pocket pistol. If you get one small enough to pocket-carry, it will be a handful for a new shooter, and if it is big enough to be pleasant to shoot, you should go with a heavier chambering (9mm Luger), for self-defense purposes.
As I said, since you liked the .45, you can handle about whatever you want, so enjoy the experimentation, and be safe.