I'm not sure that it's terribly meaningful to talk about average lengths of tour. Mine have varied from three days to eight weeks. There's no real need to train for touring, IMO. As long as you are fit enough to be comfortable on the bike for a few hours a day you can ride your way into fitness as you go.

As for costs, you can spend a lot on a touring bike and gear but there's no particular need to go mad. Say $1500 for bike, panniers, spares, etc etc? And as fr the costs of touring, they can be very low if you are camping most of the time. Certainly if you are thinking about spending $20k, even including the bike and flights to your start point and home from the finish, you could do a trip across America no problem at all, and have plenty of money to spare. In fact, you could do the trip on a credit-card basis, staying in motels and hotels and B&Bs, and still spend less than that.