Agricultural is the best trait in most cases. For the rest, it depends on difficulty and map type/size, and what win condition your going for.
I like to play Domination victory, I dont like cultural/space/diplomacy victories. Just won my first game on Sid level difficulty on a huge map with 70% water archipelago(basically continents).
Finding the best civ to win a game on Sid, was a long route of experimenting. To be honest I only ever felt I had a shot with agricultural trait. For sid-level games you will need a good start anyway, so having fresh water isn't even a question. With agricultural you can pop 10+ cities, which is pretty impossible if you dont have the trait, because the AI starts with 4 settlers and will outsettle you so hard. And the advantage doesn't stop there. Having +1 food in every city is really powerful later in the game too. In almost every game, you will end up with some coastal cities that have mountain/hills/tundra around them. Having that +1 food basically gives you a free additional hill or tundra being worked on, which does add up to a lot. Plus faster growth for all your cities throughout the game.
To me, Maya(Agri/ind), Celts(Agri/rel) and Iroquois(Agri/com) seemed the best way to go for a sid-level win with 70% water. I think the Iroquois stand out, because you start with alphabet, and the UU is probably the best. The Maya UU will probably not help you in that all-important early war. At Sid level I might even call it useless in some games. The Celts are good, but the Iroquois UU is a little better and they start with Alphabet.
I do like the Religious trade a lot, and disagree with some of the other posts on it. Going republic>democracy>communism as a game plan isn't bad at all. Democracy will give you more productive cities and more gp to keep up in research. But more importantly, you can build a larger army untill you start warring and want to switch to communism. I have noticed in Sid games that staying Republic simply doesnt allow you to maintain enough military units. Late game Communist empires simply outproduce anything. You can have 3 cores, and your allround corruption in important cities will be only 10%. Newly conquered cities will become usefull quickly. You can quickly build libraries/cathedrals, and get that culture going. Building some quick temples in Sid level will help you prevent some cultural conversions, because keeping up in culture can be a problem beside all the other issues you face against the cheating AI.
TLDR; Agriculture is best all-round trait, and Iroquois is best all-round civ at high difficulties