Picking the right metric

In plain words: The metric should match what a mistake costs in real life.

Classification: precision when false alarms are costly, recall when misses are costly, F1 score for a balance.
Imbalanced classes: avoid plain Accuracy; use ROC-AUC or F1.
Numbers: MAE is easy to explain; RMSE punishes big misses.
Forecasts: MAPE or MAE with backtesting.
Chatbots / RAG: answer correctness and groundedness on a golden set.

Tip Always report your metric next to the baseline's, so people can see the improvement.