I'm a math student in a Latin American country and I'm 31 years old. Next year I'll be starting my PhD, here, in my country. I have to say that the complete program, equivalent to a Bachelor plus Master, took me 7/8 years to complete. This was partly because I've taught a lot, working as a TA(paid positions won by contest).
My final dissertation included no original work, maybe the exposition of the topics, but no new results nor published work. Nevertheless , I'd call myself a pretty decent student. I usually recieve encouraging feedback from professors and I also have a very high GPA.
Recently, I've been considering the possibility of doing my PhD abroad, in a good school if possible, not necessarily top ranked. I wonder what my chances are of being able to do that. Are my expectations real or am I too weak for such things? Also, I think that it might be possible to get some short research/collaboration stays, say a semester or so, within the context of my PhD here. How possible is this for someone with my background?
One last possibility is switching schools in the middle of the PhD. Like, starting here, doing some progress and then moving elsewhere. I know two students who did that but they had great backgrounds. Is this possible for someone like me? I mean keeping it real, assuming decent PhD work but not assuming an extraordinary output.