Probably the quickest ending to achieve.
You will need to get the train up and running again so go to the station and talk to the station master who will ask you to clear out the tunnel , you can shoot the bandits here and then go up and clear out the room there. Return to the station master, she'll want you to clear the rubble , you need to ask 3 people to help there is a miner and rancher in clintville and you can ask either bob or richards in the south east to help too.
Once this is done return to the tunnel then the station and talk to the station master to complete the quest. Roam around or quit and reload until the train and your sibling are at the station and talk to them , you will now need to finish their quest by talking to them in the following locations
Train Station.
your burned-down home.
Fort Motors in the east
Graveyard north of clintville
Santa Anna Station go one screen to the rigth here
Lake Santa Anna, to Northwest.
and finally Santa Anna.
If you are playing as the sister you will get the end of drought achievement here too.
Now by this stage you should have a complete picture of the murderer. press Y and then right to see what he looks like, you have to find him and accuse him he's usually in santa anna station or clintville. Besides knowing what he looks like he will always start by complaining about how hot it is and moving to the mountains,
if you feel like skipping all that and just talking to every one and identify him that way feel free, I haven't tested that myself.
Anyway once you have identified him proceed to the end of the game, the key to this really is just not to do any of the major quests like rancher, oil tycoon etc.
You could also use the brother for this and try for the achievement for not being shot and more than likely swift justice for finishing the game in under an hour