The fourth enemy (Eagle Gun) you fight has a Warrior Bangle that you should try to steal if you have enough time. There’s one more fight after this and you have to fool around with some more levers, but if you’ve got a few minutes to spare it’s definitely worth trying.
After you kill the last Shinra soldier you will need to alternate on pulling levers again. Push them up using Up and Triangle at the same time, and down using Down and X at the same time. Do it a few times and burn through some quick conversations and the train will come to a stop just before Mount Corel.
The Huge Materia is yours for successful completion (but not required for the game in the least). Walk over to the townspeople and they will thank you for the service you have done for them. The townspeople will give you Ultima Materia for successful completion as well.
Wake up from your free stay in the Inn and talk to the woman in the house on the west side. She will give you Catastrophe, Barrett’s level 4 Limit Break.
Now make your way from here to Fort Condor. If you left your Highwind near the entrance to Mount Corel then you have some walking to do. If you parked it outside North Corel then you have already done your walking. Either way, enjoy the long boring walk with pointless enemies along the way.