Jab, in addition to the above, consider:
1. Diplo picks in the begining. I like populist party with maxed out diplo and +1 speed on gigantic maps. Speed is less important on medium and smaller maps.
2. Get Diplomatic Translators asap. Build your planets up with Soil, Habitat, Manufacturing Capital and maybe a Fusion Plant & Manufacturing center if you can. Then make DT your first trade good (tg) you make and don't give it away - ever. Or if someone else makes it first, then find them and trade for it. DT is the best tg in the game.
3. Routinely (every few turns?) check the diplo status of the AI. This is easily done with F5. If they go below neutral, get concerned. You will have to bribe them with a tech, tg, or money. Sometimes a ship might work. When relations get cool or worse - do something quickly unless you are ready for a war.
4 Watch for triggers that upset the AI like an influence starbase (party palace) inside the AI's sector or menacing combat ships near an AI's planet.
5. Get your trade routes out early to the nearest, biggest, baddest AI. As mentioned above, getting them all going to war against each other means they only trade with you. They love you, give you presents, and sometimes even want to snuggle.
On maso, I simply can't afford a military so keeping the AI happy is important to me. If I go war, I lose; so I don't go to war. On lower levels keeping an inexpensive military like star fighters, corvettes, or AMM can fool the AI into thinking you really have some military when you are a "paper tiger". Getting military resources helps and watching the military graph to make sure you are near the top will let you know how big you need to get. Usually number 2 or 3 is good enough to prevent extortion.
Stay at the difficult level you are comfortable with until you are ready for more challenge. The strategy changes a little bit for each level you go up and the margin for error decreases. Good luck.