I'm about to win my 5th game, which I am playing with all opponents at Normal. Like Aeonica, I started with everyone as dumb as possible and have been working my way up. Here are some simple suggestions that may help you out.
1) Don't colonize any planet with quality less that 15, until you are able to quickly upgrade it to quality 15. NEVER colonize any planet with quality less than 10, except in case of need to extend your ship range.
2) Technology is the most valuable commodity in the game. If you sell it, sell it to as many as possible to maximize your benefit. In particular, ship design is highly valued. ONLY sell to people inferior to you, Helping balance the game encourages aggressors to pick on someone else.
3) Trade with the minor races. It helps keep them in the game, which distracts the attention of the major opponents.
4) The minor races are most likely to develop trade good. Buy trade goods from the minor races rather than trying to compete for them, since it keeps you focused on what you need and strengthens the minors in their resistance to the major races.
5) When sending out colonies, sending 1 million people (the smallest number possible) is very efficient. It lays claim to the entire system and you won't have lost much if an enemy attacks.
6) I strongly suggest good alignment. Being anything else won't keep people off you, but being good nearly always neutralizes the Altarians. Plus, the Altarians will often declare war on anyone who attacks you.
7) Avoid alliances like the plague. You will get dragged into someone else's conflict, when what you want is to be producing in peace while everyone around you is fighting.
Hope this helps.