You should run wire from the alternator to the body. That's the factory ground location and the alternator case is what is part of the charging system. From the factory, grounding the alt case is plenty for the engine to make spark. It is the BEST part to ground to the battery, because the alternator is charging the battery. Grounding the engine block to the battery will NOT be more ideal for charging. It just won't.
If you really don't "want to miss anything", then you need to run a dedicated ground. I always run dedicated ground wires.
You can take my advice or not.