Traveling the world doesn't take oodles of money or massive amounts of time. All you need is a willingness to go and a destination. 

If I were to make one suggestion for starting out as a citizen of the USA, I would say go to Ireland.

First of all, Ireland is an easy place to travel to because the flights tend to be pretty reasonable as far as air travel goes. Flights can, sometimes, be snagged at close to $450 depending on the origin. Now, while that's not free it's good to know that you can set foot on the soil of a foreign land for relatively cheap. 

Even more, right now Gate1Travel.com offers trips that start at about $800 for independent travel to Ireland. Extremely reasonable!

Second, even though Ireland is home to Gaelic, everyone speaks English. You won't have to deal with a language barrier in the land of the little people! Navigating a foreign land is hard enough with their different money and different customs. Why not take away the difficulty of a language barrier.

Third of all, Irish people tend to be very fun, polite and helpful. There seems to be a pervasive trend for the Irish to treat others very well. Also, humor is one of the backbones of Irish society. I've never met an Irishman who couldn't crack jokes or poke fun.

In addition to all of this, Ireland is a beautiful land with many sights and all of them spattered with deep greenery. Furthermore, if you want to see castles, Ireland has a collection of castles that range from the fully furnish to the unrecognizably ruined. Also, there are outstanding natural sights like the cliffs that cover much of the Irish coast and the stunning Giant's Causeway.

Overall, Go!