I would strongly suggest against usign accuracy as a measure for model performance when working with unbalanced datasets. If 99% of the test set belongs to class A and my model always predicts class A, it will have a 99% accuracy despite being completely useless.
F-score (I assume F1-score) is fine as it makes a trade-off between precision and recall. If your predictions come with a probability, the area under the ROC curve (AUC) is an interesting measure, but I don't know if that's the case, so I would go for these three: precision, recall and F1-score. Use F1-score as the main reference, but dismiss any model with precision or recall below acceptable levels.
NOTE: Precision is the proportion of predicted positives that are actually positive. Recall is the amount of real positives that are identified as such. Unless there is a reason to do it otherwise, "positive" refers to the minority class