Next week will be my first time on the US and I'll need some help getting around. I'll be arriving to Washington Dulles International Airport on the 11th of this month at around 3 pm and I need to get to Charlottesville before the evening of the next day. I've considered buying a train ticket from Union Station but I've been told that a Greyhound bus could be a better option. Should I buy a train ticket or wait until the next day and take a Greyhound bus in the morning?

PS: Will I be able to buy a train ticket at Union Station without booking it?