The order in which the crimes are committed and the nature of the crime is irrelevant. You will be extradited in the order in which the extradition requests are processed. That will in turn depend upon which country lodged the extradition request first, how complicated the extradition arrangements are, how successful any legal finagling such as challenges and appeals get and a whole lot of other factors.
So, for example, if country A takes a few weeks to get enough evidence to submit a request but country B has eyewitnesses and gets their request in first, B will get you first. But if B makes a mistake in the paperwork and has to resubmit, then A gets you first. But if the extradition treaty with A requires a personal consultation between the prosecutor and the ambassador, and the ambassadorial post if currently vacant, then B gets you. But if you appeal to the courts against the extradition to B, then A will get you first. But if A tortures prisoners and country C demands that they rule out torturing you before you will be extradited and those negotiations take time, then A will get you.
And so on and so forth. There’s no hard and fast rule on this. Every case is going to be unique.