Americans (Polk): Start on your own continent that provides you with all resources you need. You are isolated from the rest of the world through the early game, but you start with an extra Wagon Train, a laborer and 4 Classial techs to help you along further (although this can hinder your very early gameplay, sorry for that). Make sure to focus on your technological progress. Either found your own religion or stay pagan until the age of discoveries.
Arabians (Rashid): Start in the desert with three cities and quite dangerous neighbors. Oases can't provide unlimited sustenance for your growing cities, so conquest into rival territories is unavoidable. Your counter-clockwise neighbors are Berbers, India, Turks, Transoxiana and Ethiopia. [Note: the desert seems to be more of a handicap]
Armenians (Tigranes): You start landlocked between France, Rome, Ethiopia, Transoxiania, Persia and Poland. Your three cities are less developed than your neighbors, but you also start with two Chariots.
Austronesia (Paramesawaran: Start off your empire on the largest island of the archipelago that holds several valuable resource hotspots. You also get two outrigger ships right at the start for early coastal explorations, and meeting many other civilizations early on.
Azteks (Tlacalel): You start on the Mesomerican Continent together with the Inka and Maya. Your first cities are in the Eastern Swamps, which are still abundant with resources.
Berbers (Abdelkader): Start in the desert with three cities. Oases can't provide unlimited sustenance for your growing cities. You can expand into Ethiopia, Arabia, India, Mali or Nguni territories, but remember that your position provides early and easy access to both the mediterranean and the Atlancific Ocean and early colony islands are not off the table. You get an advantage with regards to Slavery early on, so better capitalize on it. [Note: the desert seems to be more of a handicap]
Carthaginians (Hayreddin): Start on your secluded desert peninsula, and with an already established colony on your very own small plains continent which also holds enough dye. Barring a naval invasion, you can grow fat on trade in the early game. Egypt, Rome and Greece are nearby.
Celts (Brian Boru: You start in a fertile forested area. For access to the ocean, you have to fight through Germany, Vikings or Russia; or you may be interested in expanding into Poland, Persia and Hungary.
Chinese (Wu of Han): Start in a fertile river basin where you will have to soon compete with your neighbors: Southern China and Mongolia. Japan, Turks and Dravidia might weigh in a bit later.
Dravidians (Kulothonga): Start in a fertile grassland area with many resources. You may want to settle nearby islands off the coast as well, one of them the much marveled Pepper Island, nicely suited for you. Beware the Chinese, Turks, Arabians, Indians and probably even Austronesians who might try to grab your land.
Egyptians (Ramesses): You have a comparatively secure starting location and may finish the (already half-built) Pyramids before facing down possible invasions. Just across the mediterraniean sea, Carthage and Rome wait for you.
English (Elisabeth): Start your naval power with two cities on the British Isles, protected by reefs. To get luxuries, you will probably have to settle on the main continent. Your first rivals may be Vikings, Germany and Spain.
Ethiopia (Mentewab): You are settling the hills of a river valley, surrounded by Rome, Armenia, Persia, Transoxiania, Arabia and Berbers, of which Armenia is definitely the closest neighnor, and likely to be trouble. More coffee not in your settled area, can be found to the southeast.
France (Louis IX): Start in the fertile grassland forests south of Spain and Poland. The wine that you crave can be found with your neighbors: the Armenians to the East and Greece and Rome to the south.
Germans (Otto I): You start with two distant cities at the lake-riddled northeast of the continent. To face the threats that are posed by England, Vikings, Celts, Polish and Spanish, you better first consolidate.
Greeks (Themistocles): Your two cities are ready to either expand into the rich French plains or colonize the Spartan hinterland first. You will also face Rome; and likely the naval powers of Spain and Carthage, eventually.
Hungarians (Bela IV): You start landlocked in a forested plains terrain. Surrounded by Celts, Russia, Mongolia, Turks, Transoxianians and Persia, you will likely have to conquer some of them, or be conquered.
Inca (Pachacuti): You start on the Mesomerican Continent together with the Maya and Aztecs. The richdoms of the land are distributed in the cold hills near your cities. You have more place than the other mesoamericans, but beware of Barbarians.
India (Ashoka): Start in a fertile grassland/jungle area with many resources. You might need to fend off Arabians, Berbers and Dravidians, possibly even the Turks.
Japanese (Tokugawa Ieyasu): Start your naval power at the Japanese sea, a cold northern bay riddled with islands. While you start with only one city, a still mobile settler is tucked away in a Kobune transport to sail wherever you need it! Upon expansion, you will likely first clash with Vikings, Mongols, Southern Chinese and Chinese.
Koreans (Gojong): You start in a moderate climate with more space to expand than many other civilizations. Additionally, your neighbors are just the Southern Chinese and the Austronesians who seem not too inclined to expand quickly into your territories. The only downside here is that resources are less packed here for Korea.
Malinese (Sundiata Keita): You start in a fertile Savanna with lots of rivers and many resources, surrounded by Egypt, Nguni and Berbers. Start as with a society of pastoral nomads, then go into the goldwashing industry.
Maya (Xoc): You start on the Mesomerican Continent together with the Inka and Aztecs. Your cities lie in the vastest jungle of the world, which is still abundant with resources. You WILL want to explore the benefits of Animism.
Mongolians (Genghis): Your starting city has already a Ger built and a still mobile settler. You start in the shadow of a mountain range where Turks and Hungarians live on one side, and the Chinese on the other. Horses are to be found in both directions.
Nguni (Dingane): Live a glorious pastoral nomadic lifestyle thanks to numerous wildlife resources. Your not-too-close neighbors are Berbers and Malinese.
Persian (Cyrus): You start landlocked in a desert/plains terrain and closely surrounded by Armenia, Poland, Celts, Hungary and Ethiopia. To harness the Commercial Plantations, you will likely have to conquer your final neighbor: Transoxiania.
Polish (Jadwiga): You start landlocked in a forested grassland terrain. You are certain to encounter Spain, France, Armenia, Persia and Celts first.
Romans (Trajan): You start in a fertile plains close to Greeks, French, Armenians and Ethiopians. Egypt and Carthage are just across the mediterranean sea, as well. You get an advantage with regards to Slavery early on, so better capitalize on it.
Russians (Alexis): Starting in a snowed-in forested area close to the northern seas, you will face off Celts, Vikings, Mongolians and Hungarians.
Scandinavians/Vikings (Ragnar): Start your naval power with two cities on a cold peninsula, surrounded by maritime resources. Your first rivals may be England, Germany, Russia and Japan.
South Chinese (Xiao of Qin): Start at the coast of a fertile river basin where you will have to compete with China and Japan. You may also decide to colonize a fertile empty coastline where you will eventually clash against Korea.
Spanish (Alfonso): Start at a rich coast. Your first rivals are likely Germany, Poland and France. First build a strong land nation, later explore the oceans.
Transoxianians (Timur): You start landlocked in desert/plains terrain and surrounded by Persia, Hungary, Turks, Arabia and Ethiopia. To harness the Silk Road UI, you will likely have to conquer some of them. You get an advantage with regards to Slavery early on, so better capitalize on it.
Turkish (Alp Arslan): You start landlocked and surrounded by Transoxiania, Hungary, Mongolians, Chinese and Arabia and will likely have to conquer some of them. You get an advantage with regards to Slavery early on, so better capitalize on it. [Note: the desert seems to be more of a handicap; might need more pasture potential?]
Barbarians: You don't play them, I guess, but they have a few starting cities, too. In some cases, you can capture them early to spare a settler, but are they worth it?