Population:
Pop growth is tied pretty tightly to morale; e.g. below 54% it doesn't grow at all, and taxes (they don't DIE, they just hide from the government

). Planet quality also proves crucial for maintaining morale, e.g. a PQ20+ world can take a large population far better than a PQ15, and anything less than PQ14 you should probably think about skipping unless you've got PQ bonuses or you need the planet for range purposes.
Budget -- don't expect to keep spending at 100% unless you're exploiting diplomacy and turning low-level AIs into cash cows through what can become extremely lucrative trading, or you create a lot of starbases to boost trade routes. And be careful about that 'Purchase' button; long-term payments add up really quickly... as does ship maintenance if you go berserk with that.
Oh, and be careful what you build. Don't play this like Civ where you might want every structure at every colony. Improvement maintenance cost can really add up.
Foreign relations --
- Diplomacy helps. In particular, with recent patches diplomacy became quite powerful. Even small gifts can improve relations significantly esp. technology, and if you have a good diplomatic ability advantage.
- Trade routes give both sides income and helps keep 'em friendly.
- Having the same alignment helps.
- Keeping 'em weak helps, e.g. by bribing them to go to war against each other, they're less likely to be strong enough to see you as a victim.