It's not that I don't understand that we should start off by saying "Hi, my name is ....., nice to meet you"--- that's the standard, universally friendly way to greet someone and introduce yourself. No, I'm talking about the handshake decision; should you offer a handshake?
However, what about if you're meeting new people that could be potentially your friend/acquaintance/enemy for life?
If you offer your hand for a handshake, does that look too formal? If they aren't expecting it, the handshake will only look awkward, and make you look like an uptight and humourless human being. It's not as though you're both agreeing to some sort of invisible contract after all....it's just a mere exchange of names.
Yet, you can't just stand there and say "Hi, my name is ....., nice to meet you" without doing anything; that's just awkward in itself and probably sends out a strong "I'm anti-social" message. Unless you are trying to be anti-social, this probably isn't the way to go about introductions either.
So then, what are the other alternatives? If shaking hands makes the situation too formal, then will a wave do? Although, waving is usually reserved for a long distance type of greeting.