Do my country and the standard of my supervisor affect the quality of my PhD?
The first point: working under the supervision of an effective researcher, is certainly one of the most important criteria, if not the most important criterion.

The second point, about the country where you work, is one that many people would like to discard. However, the following points need to be taken into consideration (especially since you have given the tag of "developing-countries"):


The quality of research facilities available. This is more important for some areas of research, like experimental sciences. There is no doubt that the developed world has, on average, much better facilties.
The quality of your co-students and general research atmosphere at the probable place of work in your country. This is actually quite important as you learn a lot from other young researchers, seniors and juniors. A good university will have a better atmosphere and such universities are most often in the developed world.
The extent to which your research will get global visibility. Some areas of research are not "global" as they tackle local problems. However, many scientific areas are "global". In such a case, it is unfortunate, but true, that the country of origin of your research does make a difference to the visibility it gets.


Having made all these points, there are plus points about carrying out research in your own country.


If you do well, it brings credit to the society which you are a part of and which had a big hand in making you who you are.
Research is difficult enough without adding the burden of finding your feet in a different culture and society.


Ultimately, you will have to weigh all these factors against the quality of research positions that you have available once the application process is complete. All the best.