I am focusing on providing fast page refreshes for my visitors and I wonder where is the smartest spot to place my servers on?

I understand that the best would be to place a server in every country or even city, but that is of course not doable with my economy. I am thinking of maybe setting up three servers, one in the middle of USA (Kansas?), one in Italy and one in Sweden. What do you think about that? I don't care about Africa since they haven't even got computers so I won't get traffic from there anyway. China, North Korea etc are probably just visiting chinese websites, they barely know english anway...

The next problem is how do I redirect a visitor from Finland to the Swedish server? I don't want the visitor from Finland to be using the USA server or vice versa.