First, you should never "trust" safety mechanisms on firearms. Instead, always assume that a safety mechanism could potentially fail. They don't commonly fail, but you must always practice safe fundamentals of handling. Finger outside the trigger guard until you're on target and ready to fire, for example...
Most handguns have some form of safety. Some involve a manually manipulated control. Some have the safety features completely internal (like the drop safety inside a striker fired or hammer fired handgun). Some, like revolvers, rely solely on the need for a strongly resisting double action trigger pull.
Some firearms have multiple linked safety mechanisms. For example, guns like the M1911a1 that have a safety in the grip you must press as well as a manually operated thumb safety, or the Springfield XD series that combine a safety in the trigger with one in the grip.
For my concealed carry handguns, I prefer a firearm that doesn't require you to consciously operate a safety lever before aiming and firing. It's one less thing to be concerned about when you're under stress in a situation. I qualified for my instructor courses using Springfield XD series handguns.
For handguns that I normally use on the range, a manually manipulated safety lever is fine.