As far as I understand your question, you want the first button to light A up, the second to light B up but only if A is on, and the third to light C up but only if B is on.
Basically you need to make three T-flip flops. A flip-flop is basically a single on/off memory which is swapped every time you power the input.
ie if it's on and you power it, it goes off. If it's off and you power it, it goes on.
For the first output, A, you only need to use the button to power the flip flop and A will change.
For the second output, B, you need to build an AND gate (you can find various tutorials on this) which has two inputs. The first comes from the output from A, the second from the button, and the output goes to the flip flop which changes the state of B.
The third output, C, is the same as B but uses the third button and B's output instead of A's output.
This will allow you to light the outputs up in the order A->B->C, but will mean you need to turn the outputs off again using C->B->A. You could reverse this, but I won't over-complicate this answer with the method for that. You could, however, simply turn all 3 back off again by powering all three flip flops again manually with a 4th button.