I am a firm believer that your handshake indicates, to some extent, your character. It is certainly not the only indicator I use upon a first impression, but it holds a great amount of weight for me.
Let me say quickly that I am not talking about a bone-crushing pissing contest. That is juvenile and while occasionally amusing, indicates only immaturity and insecurity.
No. I am speaking about greeting someone in a manner that indicates interest or pleasure at the meeting. I expect to be looked in the eye and to have my hand shaken in a firm but gentle grip with a "nice to meet you". Or something along those lines.
People who greet me in this manner are those who give me a first impression of likability, believability and character.
It colors anything I may already have known or even liked about the person. I can't help it.
While I have read no studies on this sort of thing, it has been my experience, to have been correct about the character (or lack thereof) of people who have greeted me in such a manner.
Just the other day, I was proved right again, though I took no pleasure in it.
So, take a note folks, if it matters to you. Teach your children to be genuine in their interactions with others so that when they grow up and have a job interview, or meet their girlfriend's parents, their handshake doesn't have the "ick" factor.
I think no one put it more beautifully than Helen Keller.