Need Help going to Aurangabad from Mumbai

It's my first time in India. I’ll be arriving in Mumbai on January 18th at 8 PM (supposed to arrive on the 17th, but my flight got delayed). My plan is: 1. Travel to Aurangabad by train after I land. 2. Stay in a hostel in Aurangabad. 3. Visit Ellora Caves, then return to Aurangaba at the same day. 4. Go back to Mumbai for my flight home at 12:40 AM on January 21st. I prefer trains over buses or taxis. Can someone guide me on: 1- Which train to take from Mumbai to Aurangabad and back? 2- Which stations I should use in Mumbai and Aurangabad? 3- How can I book train tickets? Any advice on timing or other tips would be great.