You don’t sound stupid at all. In fact, your question is one that everybody has probably wondered at some point.
The correct answer is “a couple of minutes”; the simple explanation is that “a couple of” is an idiom:
"A couple minutes" (without "of") is considered informal, i.e., inappropriate in formal writing.
In closing, spend a couple of minutes staring at this GIF, and then do something productive with the rest of your day.