No experience with the wine train but knowledgeable regarding the bus to the coast.

Take a taxi or the red (main) Metro line to either the Universidad de Santiago or Pajaritos Metro stops. Bus Terminal Alameda is above the Uni de Santiago Metro and can be directly accessed from the Metro. Terminal Pajaritos would be more convenient for Viņa as nearly all Turbus and Pullman busses (the two main intercity domestic bus companies) start at Terminal Alameda and then stop at Pajaritos before proceeding directly to the bus terminal in Viņa.

Price will be around 3000 or so pesos; seats are assigned (try for seats away from the back where the baņo is located); busses leave every 15 minutes and take around 1.5 hours to reach the coast; baggage can be checked into the hold (this is safe); and speaking and understanding basic Spanish is a plus to make the process smooth.

Be especially vigilant with your personal belongings at the bus terminals and do not put anything important or valuable in the storage area above your seat. The stuff on your lap or at your feet, make sure they cannot be easily pilfered or snatched if you snooze.