In general, if your starting point has a lot of cows, wheat, dear, stones, ***SALT***, horses, by a river, by a mountain, it's a strong start.
Alternatively, a desert start with some oasis and hills is also fairly good... provided you are the only one starting on desert (i.e. no one else takes desert folklore and petra).
Being close to several aggressive AIs makes the game a lot harder. But what I feel is the HARDEST is to be sandwiched by one aggressive AI (e.g. Monty, Alex, Genghis, Attila) and one expansive AI (e.g. Washington, Napoleon, Hiawatha). I've encountered this scenario several times and it feels hopeless as the expansive AI grows like crazy but I can't punish him because Attila has been parking his rams in front of my capital for 30 turns.
I am probably the only one who thinks like this, but I dislike settling on hills because I like to be able to build wind mills (obvious exception: Austria). I feel that wind mills are pretty broken and worth sacrificing one hammer in the early game for.
EDIT: I feel that what I had here
http://forums.civfanatics.com/showthread.php?t=488410 was a pretty good start. I had 4 salts near my capital, not too close to any of the AIs, and lots of wheat around me (although not close enough to the capital) for some easy expansions. It would be even BETTER if the stone was a bit closer and not on tundra.
Salt is an awfully imbalanced luxury. Sometimes, it makes an Emperor game feel like Immortal (when an enemy AI has a bunch of salt). Other times, Immortal feels like Prince (when I have a lot of salt). The only other luxuries that have such a big impact are Gems (Gems on a hill/river tile is a ton of gold) and Marble (wonder production bonus affects my Emperor games, and games below that; when I play Immortal, and the odd times I go for Deity, the wonder production bonus is not so impacting).
The other really great start is when I have a bunch of whale or crab tiles. Throw a harbor on it, along with the belief for +1

per fishing boat, and for good measure the Colossus (if possible, depending on difficulty), and watch that city blossom.
On Pangaea it is an absolute nightmare though. I usually don't reroll maps, but one of the conditions which will always cause me to reroll is when I get a coastal start and there are two different luxuries in the ocean. I feel that this is borderline unplayable on Pangaea unless I am playing Carthage (it's a struggle even with Carthage).