The most important handshakes are when you're establishing a business contact or relationship with a person you're meeting with for the first time (and thereafter). Other handshakes are for social reasons not related to business but still just as important. It's important for deaf people to understand the value of a handshake along with other social cues like eye contact and saying the right words. In other words, strive for the "perfect" handshake and avoid being known as a person with a fish-like, limp handshake that no one wants to shake it with. There is a time and place on how to do the right handshake. Not every handshake has to be a strong, firm one. Social settings dictate the kind of handshake needed.
Of course handshakes between men and women are different, especially when it comes between two opposite sex shaking hands with one hand normally being the bigger hand of the smaller one. And those with small hands, there are ways to counter strong (even crushing) handshakes of a bigger or stronger hand during a handshake. There's a technique in a handshake where you won't feel overwhelmed with an overly aggressive and crushing handshake by an ego driven idiot. A technique that can even prevent hurting your hand. Maybe I'll show you how the next time around? Meanwhile, watch that handshake!