As others have said, trains are virtually nonexistent. THe intercity Bus network (KTEL) is modern and very efficient and used by all classes of people, tourists and greeks -- some Americans from certain areas have little experience of intercity busses, but should be aware that they are a big part of transit system on Mainland, Peloponnese & large island like Crete (which is almost a country in itself)
You need to look at a couple of good Guidebooks to understand how travel in Greece really works; not enough tiime or space to give you a complete briefing here. And also, you need to tell us how many days you have (NOT counting arrival day or departure day) because advice would be very different if y ou have only 10 days or 21 days. Browse all the guides in your local library, then buy a copy of the one(s) taht you find most useful.
A satisfactory trip of say, 15-17 days, may involve domestic flight(s), several ferry rides, a KTEL bus, AND car rental for a few days. Example: • On arrival, fly domestic to farthest island (Crete?); spend 4-5 days there, using KTEL bus or car rental to explore • Ferry to Island #1, use local bus or a days car rental there. • Ferry to Island #2, use local bus, taxi or walking • Ferry or domestic flight back to Mainland (ATH airport) • Car rental to mainland destinations such as Delphi or Argolid area (OR KTEL bus) • Athens Finale: NO car rentals (impossible traffic & parking, besides, major landmarks are all grouped closely for walking). • Departure = taxi or express bus or Metro to Airport. I have done trips similar to this a number of times.
See what I mean? Transportation is complicated! And Logistics are a priority before Accommodation. FIRST, figure out which are your "must" destinations feasible within your trip length (keep in mind changing locations, no matter how close will eat up half a day each time). NEXT: Learn about bus schedules, flight availability (mainly Aegean/Olympic or Sky Express), ferry schedules... and on a map insure that your wish-list of places can be done in sequence (i.e. -- it makes no sense to want to go to Corfu and Rhodes, in the same trip.... look at a map & see why). STAY FLEXIBLE: Don't Lock yourself in to Lodgings: Always take the room rate that provides for cancellation/date alteration without penalty. Once you've developed a sequence, and know the transport options to get you from place to place, only then do you book lodgings.
When you have a feasible sequence, we can help you with transport suggestions, and (if y ou are specific about dates, and budget ranges), also about hotels/pensions etc. Dive in, get your feet wet (metaphorically), and planning can be fun! Best of Luck! I hope to be there next Spring as well.
PS: You rent a car when you reach a destination, you don't rent a car on arrival in Greece & try to take it on ferries. No can do.