Ride with no cleats and no toe clips. In other words, just plunk your feet on the pedals. You'll get used to NOT pulling back on the pedal. You may find yourself "ankling" to keep your feet on.

This practice will serve you for when you have toe clips.

The weird thing is that when I ride with toe clips, I still habitually twist my feet before pulling out.

With toe clips, I usually keep the left strap tight-ish and the right strap loose. I put my right foot in second and take it out first and leave my left foot in when I'm waiting at a stoplight. Be sure to make it easy to adjust at least your in-and-out strap with your hand while you're on the bike. But really, you don't have to tighten it. I pretty much never do.