What’s the proper way to compare a String to an enum value?

I’m gathering from your question that userPick is a String value. You can compare it like this:

if (userPick.equalsIgnoreCase(computerPick.name())) . . .

As an aside, if you are guaranteed that computer is always one of the values 1, 2, or 3 (and nothing else), you can convert it to a Gesture enum with:

Gesture computerPick = Gesture.values()[computer - 1];