Cleaning up after you have finished every coat of paint is time consuming and really unnecessary. A few years ago I was taught that wrapping your brush in plastic wrap stops the air getting to the paint and therefore it doesn't harden. You only need to clean your brush at the end of the job. Whilst hunting for some suitable wrap I realised I was already wearing it!
Since getting hold of a 100 pack of disposable gloves I've been using them to keep my hands clean(ish). They work really well for painting! So, if you hold the brush in the palm of your hand. Using the other hand pull the wrist over the brush and your hand out of the glove. The bristles should be covered by the glove.