For those pilots who want a to follow a different path to the cockpit - my hat is off to you. Living in a foreign culture is a fascinating experience and you will be forever changed by it. It seems to me that most pilots here in the USA would rather not live away from the states and their path to their goal is to proceed direct at best forward speed - not that it's a bad thing! But to enjoy the scenic route to your destination can be a wonderful thing.
Most American pilots aren't working outside the USA for two specific reasons. 1. they want to live IN the USA, not outside it. 2. They don't have citizenship in the country that the airline is based in.
Half the battle to get hired overseas will involve local citizenship (or right-to-work). Then you will likely have to have a local pilot license - JAR ATP in Euroland, not the ICAO atp that's issued here. After that, things become more flexible if you have some hours and can fit well in the local culture. The local culture may be the bureaucracy that is endemic in Europe, or the flexible sense of time in the Caribbean, or the rigid conformity of Japan. Which by the way, I mean no disrespect, all those places are great, it's just how they do things.
I would suggest considering using your CFI to instruct overseas, maybe Europe and pick up a second language fluently. Also, Africa offers low time guys a chance to fly tourists in SE aircraft. You'll certainly gain proficiency quickly. Alaska is also a good place to pick up time, though you may have to work ramp, pump gas at the same job first.
If you are single, stay that way because you can quickly jump on an opportunity. You can have a spouse, kids later when you're older, more stable in your job, and have a few more dollars in your pocket. I didn't meet my wife until I was 26, because I was flying here, there and everywhere and am glad it worked out like that.
Go for it and never look back, the world is your oyster!