I want to generate DC voltage by a transformer, a rectifier and a series regulator. What should I be careful about?

Common

The secondary of transformer might be occurred more than 2 times output voltage when the primary of transformer is cut off immediately. Therefore, it should be connected IC of the high breakdown voltage to the secondary of transformer.
If you connected a low breakdown voltage IC with secondary, it might be destroyed the IC. You should be checked by an insertion-pull out test for the connector of primary side, or connect a surge absorber on the secondary of transformer.