One of the main reasons to use a ROC curve is for imbalanced (usually binary) datasets. A more intuitive way to look at FPR is FP/N. The curve tells you the fraction of false positives you are going to pass through for any given TPR (recall, sensitivity). If the fpr you care about is tiny, you can focus on the left side of the curve and ignore the right side.

It's also useful to sample the roc curve at recalls you care about. e.g., how many false positives am i passing through for a TPR of 95%?

Lastly, in my experience, AUC correlates highly with an improved model because most of the right side of the curve doesn't tend to change much and sits close to 1 in situations where you're just trying to improve the left side of the curve. If it doesn't, then you probably just need to change the number of thresholds you're sampling when computing auc.

Whether to use roc or precision-recall depends more on the type of problem you're working on. Obviously precision-recall is better for information retrieval, because you care about what fraction of the information retrieved at a given threshold is useful. Roc is better if you care highly about the raw number of false positives you're letting through.