NFHS defines it
2-14-1
A fielder's choice is the act of a fielder with a live ball, who elects to throw for an attempted putout or to retire unassisted any runner or batter-runner, thus permitting the advance of another runner(s). Scorers use the term in the following ways:
a. to indicate the advance of the batter-runner who takes one or more bases when the fielder who handles his batted ball plays on a preceding runner;
b. to indicate the advance of a runner (other than by stolen base or error) while a fielder is trying to put out another runner; and
c. to indicate the advance of a runner due to the defensive team's refusal to play on him (an undefended steal).
Fed also says
9-2-2
A base hit is creidited to a batter when he advances to first base safely: ...
c. because of a fielder's choice when a fielder attempts to put out another runner but is unsusccessful and the scorer believes the batter-runner would have reached first base even with perfect fielding.
So, although you are asking two questions: what is a fielder's choice? and what is a hit? I think these rules answer your situation... per federation rules. I assume a score keeper for an OBR game would use the same criteria.
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"There are no superstar calls. We don't root for certain teams. We don't cheat. But sometimes we just miss calls." - Joe Crawford
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