If a batter hits the ball to shortstop and the shortstop throws to third base trying to get the lead runner but all runners are safe is this scored as a hit or a fielder's choice?

The play is scored as a fielder's choice, regardless of whether the preceding baserunner is out or safe. Any time an infielder attempts to put out a preceding runner other than the batter, it is scored as a fielders choice. From Section 2, Definition of Terms in the Official MLB Rule Book defines a Fielders Choice as follows: FIELDER'S CHOICE is the act of a fielder who handles a fair grounder and, instead of throwing to first base to put out the batter runner, throws to another base in an attempt to put out a preceding runner. The term is also used by scorers (a) to account for the advance of the batter runner who takes one or more extra bases when the fielder who handles his safe hit attempts to put out a preceding runner; (b) to account for the advance of a runner (other than by stolen base or error) while a fielder is attempting to put out another runner; and (c) to account for the advance of a runner made solely because of the defensive team's indifference (undefended steal). It is scored as a fielder's choice. rule 10.05(f) A base hit shall be scored when a fielder unsuccessfully attempts to put out a preceding runner, and in the scorer's judgment the batter-runner would not have been put out at first base by ordinary effort. You won't find many official scorers that will give a batter a hit on that, unless the batter would have beaten the play out anyway. (i.e., a slow roller, high hop, deep in the hole, etc.) In the context of the question posed here, we almost have to assume the question was asked to imply that it was a routine, well-struck, fielded ground-ball and the shortstop made a conscious decision to attempt to get out the lead runner.