If the other person is standing I would stand up - or at least start to rise - while shaking their hand. It looks to me like otherwise you are not treating them as your equal, informal situation or not.

If the other person is also sitting, I would also stand up while shaking their hand if they rise. And I have to note that when two people are sitting down there is already a rapport established, which may make shaking hands superfluous - depending on the situation.