Particle automatically spread from the center, with the default settings. So that shouldn't be too tricky. You'll need to keyframe the emitter to turn off after a short while, else it will just continue to emit particles. Then set the Opacity Gradient so that they fade out across their lifetime.
If you want a pinwheel, try starting with this preset
. Or this preset.
Take a look at how they are constructed to see how you could get similar results when building your own effects.