Depends on what you mean by "fly in the States" - do you mean train in the US or go and work in the US (or both)?
If you want to work in Europe you will need an EASA licence, if you want to work in the US you will need an FAA licence (plus the right to live and work in the US). In Europe there is a culture of recruiting low-hours cadets direct from training, though competition is fierce. In the US the culture is geared more towards newly qualified pilots building hours as instructors etc before getting their first multi-crew job.
Your best bet would be to look at the experience requirements and qualifications for the types of jobs you are aspiring to and then work out how you might go about meeting them. And if you can't find the type of job you want advertised then that will tell you another story .....