Rock is the most common throw. Not by a little — by enough that it shows up consistently across large studies, multiple countries, and different player populations. If your default opening move is Rock, you're in the majority, which is a useful thing to know because it means your opponent is probably throwing Paper to counter you.
Rock players tend toward directness. The closed fist is the natural starting position — it's what your hand already is before the count — and players who don't think much about their throw default to it. In casual play, Rock is often a tell for low strategic engagement. In competitive play, leading with Rock can be a deliberate misdirection, playing into the expectation in order to exploit the counter.
Paper players are either thinking about the game or not thinking about it at all. Experienced players open with Paper because they know Rock is the most common opener and Paper beats it. Complete beginners occasionally land on Paper by accident. In a tournament context, a Paper opener signals that your opponent has done at least some preparation. Don't assume the Rock bias applies.
Scissors is the rarest opening throw and the most interesting one. Players who open with Scissors have usually thought about the meta-game: they expect their opponent to throw Paper (to beat the expected Rock), so they counter that expected Paper with Scissors. It's a second-order read, and it either pays off or gets crushed by the rare opponent who opens Rock sincerely. Scissors openers tend to be either experienced players running a gambit or overconfident players who've learned one strategic principle and deployed it everywhere.
What your throw says about you gets more interesting over the course of a match than it does from a single opening. The win-stay/lose-shift pattern — winners repeating, losers cycling predictably — reveals personality more than the opener does. Players who fight the pattern, who consciously vary their throws after wins and interrupt the cycle after losses, have done the psychological work to suppress their own behavioral defaults. Players who run the pattern without realizing it are playing against themselves as much as they're playing against you.
The best throw to make, strategically, is the one your opponent least expects from you. That requires knowing what you usually throw, which requires enough self-awareness to have watched your own patterns. Most people haven't. Most people throw what feels right in the moment and are mildly surprised when it doesn't always work.