What are the best businesses to start in a third-world country?

Sorry Sir; Are you asking a universal business type that works in a third word? With do respect would you refine your question? Their is nothing as such that works in third world. would I say food industry? The Americas and western do not eat. Would like me to say armament factory? The Major producer's of armament are the wealthy countries. Or tell us or give us a hint to answer ur question.

Definitely, any business has relation with food such as restaurant or resort

It will really depend on the country itself, the atmosphere and the population, for example some third world countries need big investment to develop their agriculture to reduce their food dependency. in some other countries, people are still using old technology, for example TV's and mobile phones, so installing a small factory in one of those countries would be beneficial. An other project which is too risky, transport of goods in dangerous zone, like Iraq or Afghanistan. 

From food manufacturing to pharmaceutical ( medicine ) , as both are essential.