1. If playing a mission that gives you access to a new unit, build and support only that new one. The missions will be much easier that way, especially those that are on some kind of timer (lava surges, walls of fire, night invasions, etc).

2a. Buy unit upgrades from the armory carefully; you can spend hundreds of thousands on units you'll never use again.
2b. Buy mercenary contracts. You'll need them.

3. Remember to take advantage of the research units and abilities. I restarted the final mission three times before remembering to use one of my researched buildings, and beat the mission easily. Yes, they can make that much of a difference.

4. Try to get all of the zerg/protoss research points; excess points after the cap sell for 10,000 each.

5. Science Vessel > Raven