Theluin has some good tips there. If you like more challenge, you can change the starting level, setting your starting level at "Starting" and the AI's starting level at "Mature". I've found giving the AI more money (with higher difficulty settings) does not necessarily help all that much, since I usually get all their money in tech trading anyhow.
Question to Theluin: Is that actually hurting you more than the AI? I've never messed with the corruption slider, but I wonder, especially with "mature" galaxy settings: The AI would potentially be making money / revenue from colonies, whereas you (the player) almost never do (I have tax at 0 for huge portions of the game for everything except conquered planets and my own HW), making corruption almost a negligable factor -- but I play in galaxies, so far, in which EVERYONE starts as "Starting". But if you start on "starting", and the AI has a lot of developed colonies it is not earning income with (b/c of high corruption), this is perhaps a bonus for you?