equipment recommendation - What should I look for when shopping for my first mirrorless camera?

I'm looking to buy a new camera. I've looked at What do I need to consider to choose between dSLR, mirrorless, or a compact as my first "serious" camera? and decided that mirrorless is right for me. But what next?

What should I be looking for when shopping for a mirrorless interchangeable lens camera (and what should I not be concerned with)?