In canon Gibbs is basically a good guy at heart, when he's wit Ducky he's a lot more humorous and also with Abby who he seems to almost have a sibling relationship with. With the others he's not so open but still makes jokes, but he's also very serious about his job, doesn't tolerate fools or interference and will stomp Tony and Kate down if they're messing around too much, but he's also ferociously loyal and very determined. He clearly cares very much for his team even when they annoy him. Obviously his relationship with Mac is going to be more like his canon relationship with Ducky because Mac is his superior officer rather than a direct subordinate like Tony or Kate.
He does have a nice line in humour even though it's not always friendly - he claims the second B in his name is for Bastard and tells a Mafia guy threatening him that he has no family, but he does have three ex wives 'whose names and addresses I will happily give you'.
Wow, probably more than you wanted to know lol. Gibbs is without doubt one of my favourite characters on TV, and not only because he's hot. :)