When we retrain a model, we want to see if it learns better from new data. Key metrics to watch are validation loss and validation accuracy. These tell us if the model is improving on unseen data, not just memorizing old data.
Also, watch precision and recall if your task is classification. They show if the model is correctly finding important cases (recall) and avoiding false alarms (precision).
Finally, track training time and resource use to balance model quality with cost.