Which of these sentences is correct?
They create comfortable conditions to transport goods around the country.
They create comfortable conditions for transporting goods around the country.
Additionally, if I don't write about any specific country, do I need "the"?
Those two sentences are both correct. They mean the same thing, and are interchangeable.
If you are not writing about a specific country, you still need to use some article with "country". You can say, "... around a country," but just "... around country," is not right.