Ditto on much of what has been already mentioned.
A good place to start is with a revolver. They are easier to manipulate with more inherent safety than most semi-autos. The calibers you mentionaed are also good choices. A .357 weapon is more versatile since it will shoot .357's & .38's. Ammo is plentiful and affordable. Many good revolvers are out there, usually for a good price if you shop around.
Shoot as many different types of revolvers as you can. Try different grips, if possible, too. One gun might be uncomfortable with factory grips, but much better with a different set. I personally like Hogue or Pachmeyers, depending on the gun and/or design.
How do you plan to carry this gun? Concealed? In a car? In the house? All these are important considerations when selecting the type/style/size of the gun. For concealed carry, go with something small and light. For carry in your car, or in your home, you can go with something larger. Generally larger guns with longer barrels will transfer less recoil to the shooter and will be more accurate with higher muzzle velocities.
My best advice, go to a firearms trainer and have him/her help you select the best choice for your needs. From there, select the gun that you like best in that category.
Good luck. :smile: