The choice between the rebels or government is just for what events and quests you get to reach the end result, but the result will be the same due to outside factors influencing the situation. Therefore, you can pick whatever you prefer without having to worry too much about it.
You're probably on the step where you have to go to the bottom right corner.
A full list of each step can be found here: https://renryuu.miraheze.org/wiki/Riddles#Sparky's_mine_cart_challenge_2