"Trip" is the right one for a beginner to learn and use.
"Journey" and "voyage" both convey ideas of grandeur. "Journey" suggests a long, complicated trip. "Voyage" suggests traveling by sea--a major trip from point A to point B, perhaps with difficulty or danger--not a pleasure "cruise." In modern times, they are more likely to be found in book titles than in plain writing. "Voyage" is outdated because we rarely make voyages, we take flights!
"Voyage" is a loan word from French. We've borrowed it completely, and pronounce it VOY-adj, i.e. we Anglicize the pronunciation.
In the U.S., if friends are going to be traveling by ship, typically on a "cruise ship," when we are saying goodbye to them we are likely to wish them "Bon voyage," using the French phrase with a rough imitation of French pronunciation: "Bawn voy-AZH."