In sklearn's classification report, is f1 the best accuracy measure?
You got recall incorrectly. It does not mean "correct out of all the samples".
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Looking at the image,

$\hspace{50mm}$ Recall = $\frac{TP}{TP+FN}$

It is explained here.

From the above documentation, you can also see that you can modify your F-beta score to suite which to weigh more, precision or recall. Therefore, f-score would give you an overall of how good your classifier is, but if you need to know at which samples your classifier fails, you need precision and recall.