dnd 5e – What skill proficiencies can a Variant Human choose from at character creation?

With the Variant Human Traits option, you get to choose one skill of your choice, period.

The D&D 5e PHB on p. 31 states:

Skills. You gain proficiency in one skill of your choice.

That is the end of the description of this option. If there were meant to be a restriction to your character’s class list of skills, it would say so. But the text mentions nothing about class skill lists. So, there is no such restriction.