[Pretaco]

x2 on vacuum leaks.

A lot of the time the vacuum leak will go away after warming up due to the metal parts expanding and sealing the leak back up.
Pinch off your brake booster hose before starting it one morning to rule it out.
The cold start injector won't make it idle bad, just makes it take longer to start on first start, but once it does start the injector shuts off. If it cranks for 15-30 seconds before starting, then look at that injector.
Do you have a check engine light? If the engine coolant temp sensor is bad, the ecu uses 180 degrees as a failsafe so that the engine will still run, but when it is cold, it will run like crap.
Hate to say it, but a blown head gasket will make a car run like crap when first started, but then clear up as the coolant gets burned out of the cylinders.