First I would find a local range that has rental guns or a gun store that has a range. Going to the range with a friend who has a collection is also a good option. Then shoot a variety of handguns.
Larger handguns of the same caliber will have less recoil and be easier to shoot accurately with. Smaller handguns are easier to carry. Revolvers allow for pulling the hammer back with your thumb then having a very light trigger release. Semi automatic handguns typically have a longer, heavier trigger pull combined with a larger ammo capacity.
Most shooters will have a tendency to anticipate the shot and depress the muzzle to counter the expected recoil as they pull the trigger. This results in the bullet hitting below the point of aim. This is particularly true with the long trigger pull models that most of us carry. The best way to overcome this is to practice dry firing your carry gun. To do so make sure the chamber and magazine are empty then rack the slide or pull back the hammer, aim then pull the trigger. The more you repeat this the less you will anticipate the shot.
As for which gun to carry my recommendations are different than others. For carry I recommend something from
KAHR. The PM9 and CW9 are small, light weight, highly accurate 9mms that conceal easily in your pocket or in a IWB holster. KAHR's products are designed, tested, serviced and manufactured in the USA.
The Ruger LCP mentioned above is a well made inexpensive option. I personally have a dislike for them as they are little more than a copy of a Keltec product that was designed and is manufactured in Florida. That is an issue with the manufacturer not the product.
For home I would recommend a Springfield XD either in 45 or 9mm depending on how you feel about recoil. I have two XD45s that each have thousands of rounds through them without a single failure. They are well built, reliable, accurate enough, eat any ammo you can find and have a safety on the grip that ensure the gun is held securely before functioning. This safety avoids many negligent discharge scenarios and reduces the ability of children to fire it.
Most importantly, whatever you get practice and actually carrying the handgun are the keys to being able to effectively use it if needed.