After you've decided on the handgun that's a good fit, you need to purchase ammunition for it. Step number one: Always follow the manufacturer's guidelines as far as recommended ammunition. Handgun ammunition can be found in Standard, "+P" and "Magnum" configurations. Ammo loaded at +P velocity has a higher pressure than standard rounds. Magnum ammunition has the highest pressures found in handgun ammunition. Higher pressure translates to better effectiveness downrange but it also puts more pressure/felt recoil on the shooter's hands and the gun.
Most modern firearms are built to accept the pressures of +P ammunition but a steady diet of such ammunition may wear on the gun over time. NEVER attempt to load Magnum ammunition is a gun not chambered for such loads.
Unless you are involved in some type of precision marksmanship competition, your choices for handgun ammunition will fall into two broad categories: practice/training or personal defense.
A quality defensive load will have a controlled expansion bullet. These come in many varieties but all are designed to expand/open up when they strike something solid like animal tissue. The reason for this is two-fold, expanding bullets reduce the chance of the bullet passing completely through the target and they also will potentially do more damage to the target thus reducing the number of rounds it takes to neutralize the threat.
Some of the premium components include nickel (silver) cases, sealed (moisture-proof) primers, and flash-reducing propellant powder. Because defensive ammunition is built from premium components it is naturally more expensive. In this case, you get what you pay for.
Training or practice ammunition is purposely built from less expensive components. By using less expensive components the manufacturer is able to reduce the consumer cost thus allowing you to shoot more for less money. Practice ammunition will be loaded with full metal jacket (non-expanding) or solid lead bullets and the cases will be standard brass.
When it comes time to choose ammunition keep in mind; premium defensive ammo goes in the gun for that "just in case" moment. Less expensive training ammo is what you will take to a class or out to practice.
If you are completely stumped as to what type or brand of personal defense ammunition to purchase, find out what your local police officer or sheriff's deputy is carrying. That's not a perfect answer but a good place to start.