If you don't feel like spending 5 hours in the train, the alternative is to take private bus lines. It will get you there faster but not cheaper (but not by much). Di Fonzo, a company whose seat is in Vasto, will take you there in over 3 hours: http://www.bus.it/difonzo/index.htm where you can book your trip.
If you are in Rome, you can buy the ticket or make a reservation (highly recommended) there:
Agenzia Piccarozzi - C/o TIBUS - Stazione Tiburtina - Tel. 06.97749140.
The other possibility is to take the ARPA bus from Vasto to Chieti then to Rome (arpaoline.it). The bus from Rome leaves at 2:30 and 5:30 PM. The bus from Vasto to Rome leaves at 7:30.
Unfortunately, none of these companies tells you where to wait for the bus! Although betting on the train station is probably safe, it's better to get in touch with them and ask.
As a rule of thumb, you can find a lot of information at Roma Tiburtina, where most buses linking Rome to other parts of the country are leaving.