The purchasing of a car and then selling it before you leave idea sounds great at the onset, but in the big picture could be more hassle than it is worth. The previous mentions of registration, insurance, breakdowns, inclimate weather conditions don't seem worth it to me. Not to mention getting an international drivers license, the outrageous price of gas, learning to drive on the "other side of the road" and the sheer fact that it would be too darn easy to get lost and could be one very lonely trip for a solo traveler.
Plus....what if you couldn't sell the car right away before you had to leave?
I'd nix the bus and opt for the east/west train deal myself. Busses just seem cold and impersonal. On the other hand, the train sounds much more comfortable, you don't have to stop in every little hodunk town along the way and just the sweet rhythm of the rails beneath you brings a bit of magic to the trip. I am such a sucker for the romance of it all though and trains seem very romantic to me.
Probably because I grew up with a daddy working for an airline and
every darn vacation we ever took, we
had to fly. I feel like I missed so much of the "in between" sites.
Go for the train....enjoy the beauty of the country without having to worry about your next fill up or which exit you should have taken. Every big city you plan to visit has good inner city transportation systems once you get there.
Go train, go train, go train! And even if you don't, have a wonderful time!!