Stick with it – it really does become second-nature pretty quickly. You'll soon find you don't need to concentrate on what you're doing all the time, which frees the brain up for thinking about all sorts of other cr@p. 😀
As for clipping in, double-sided pedals make it a lot easier. I use Speedplay Frogs, and just clip in with my right foot, set off, and then let my left foot follow the pedal round until it's connected too.
Think the only issue I regularly have is if I have to come to a complete stop, and can't engineer it so the cranks are already in the right position to set off again – hoicking the back wheel up and spinning them round until they are can be a bit of a pain, especially in traffic. Suppose I should really learn to trackstand… 😳
And don't stop pedalling!!! 😉