Depending on the application, I prefer the 45 Auto. It has more than enough stopping power and low velocity which cuts down on over penetration. It is expensive to practice with, and takes a fair amount of practice to shoot well, so if funds are low this is probably not your best bet. 9MM has served as a very useful and successful self defense round. Plus it is very cheap to buy ammunition for so you can get a lot more practice in. It is also a light recoil round and its magazine capacity in most handguns far surpasses that of the 45 Auto. A little more info on the application would be helpful but I hope the info I have given you helps.
That's a much more complex question than it seems. So I'll give a few basics... If you aren't an accomplished shooter, stick with a Revolver, they're simple & don't jam. .357/38 is an excellent calibre if you buy good self defense ammunition.
I carried a S&W .357 for years. Excellent weapon. (for home defense, stick with a shotgun. Remington 870 is an excellent choice.)