I'm surprised no one has mentioned chess.com's Game Explorer yet. It can't select the statistically most successful move automatically, but it shows the stats for each move. You just need to do little bit of simple calculation, and then click on the desired move yourself.
You must upgrade to premium memberships to go beyond 3 or 4 moves.
You basically described an opening book that is generated from a database. Most engines let you select an opening book and you can force the engine to select moves from the book,