This is a page for the best countries to start, both by popularity and personal experience.
India: A very common Plague inc. favorite. The country borders 3 other heavily populated countries. India has a fairly busy Airport and and a very busy seaport. With over a billion people inside its borders and good conditions for a new plague, it seems one of the best countries to get a plague up and infecting a huge population very quickly.
Saudi Arabia: This place can practically be defined as a hack for your game. It borders 5 countries and has a seaport that can infect several more. But this country has a great selling point in its Airports. Their airplanes fly to every other Airport in the world, and while you evolve Air 1 and Air 2, you are also increasing the infection rates for the arid country. It seems one of, or maybe simply the best choice to evenly distribute the plague around the world.
Russia: The country is your best weapon against Greenland, start there and evolve water 1 and you will probably have it early in the game. Russia also borders 9 other countries and has fairly busy airports and seaports. Seeing how your next choice for infecting Greenland is Norway, a nightmare in it of itself to infect, the thought of making Russia unhealthy as soon as possible sounds highly benefical.
Egypt: Similar concept to Saudi Arabia, main differences are the country is poorer and easier to infect, the airports are sadly are not as busy, and that the extra seaport only gives a couple extra infected countries. However, a poor country with airports and seaports is quite rare, exclusive to Egypt, in fact.
C. America: This is a personal favorite of mine. Although the country only has two bordering countries and no airports, it can get your plague very far, very quickly. Its seaports go to Argentina, to the USA, to Australia, and to multiple European and Asian countries. Depending on which game mode you play, your best option might be to try to get the best out of the Panama Canal.
What is the worst country to start in? One that comes to mind for me is Sweden. They have no airports, a mostly inactive seaport, and are not only a rich country, but are bordered only by two other rich countries. Not only would you likely be detected quickly, but by doing so you would not have gone far at all.