If you have good board scores and can hold a conversation, don't be intimidated going for what's considered the more competitive residencies. When I was on The Rock there was a steady stream of advice from admin of "playing it safe." They meant well and this advice probably holds true for 1/2 - 2/3s of the class, but if you're a competitive applicant don't shy away from the competitive residencies just b/c you're from Saba (or any other foreign school). It's not easy but it can be done.

And, yes, it helps if you have family connections, but I'd argue that most got their positions based on their on own merit and by making their own connections while working hard in the hospital.