When you're pulling away, you need to consider who might benefit from your signal. It's important that you don't signal if you have a car approaching behind that you intend to wait for - A signal may worry them that you're going to pull out on them. Signals are handy for other road users that aren't passing you, such as people in parked vehicles, cyclists, pedestrians and oncoming traffic.
Warning - Signalling at the wrong time may cause traffic that have right of way over you to brake when they wouldn't expect to. Think about your signal timing so you don't create a negative reaction from other road users.
WHO SHOULD YOU SIGNAL FOR HERE (THE CYCLIST IS STATIONARY)?
You should wait for the red car to pass before you signal and then signal for the cyclist because you don't know when they might pull away.