The norm for rainwater systems is UV or Ozone. Chlorination, RO, and distillation are also options however, not commonly used in rainwater systems. A 1 micron filter will not remove all bacteria, but most. I have read publications by the CDC that it needs to be a .3 micron to remove almost all bacteria. Of course this would not remove viruses.
The linked article below gives a good overview of the various options. I have also linked a book below that is very useful, with great charts and tables.
As far as carbon you are correct. I only recommend them when more removal is required.
I recommend .25 micron (sediment removal), a 5 micron (most bacteria and dust), a granulated carbon filter (chemicals, chlorine, bad smells and taste) and finally a UV light (disrupt DNA of bacteria making it harmless). This combination removes bacteria, most viruses, and cysts.