I've had two essays in Brain, Child.
I always look at the writer's guidelines and follow them exactly. If they say they want electronic subs, send it like that. If they want hard copy, they'll say so. It also helps to know the publication really well, so you understand just what they are looking for.
Persistence is also key! I had a few rejections from B, C before they took my first essay.
As for cover letters, I think they are a good idea, but keep them very short, including a brief description of your article:
"Here is an essay I hope you'll consider. 'My Big Mouth' is the account of one mother's repeated experiences of embarrassing herself at the local playgroup, and how she managed to recoup her friendship losses."