Don't overdo it on the estimate percent either. Low values (1-3%) with block-based sampling often produce good statistics, particularly on something like an audit table from which there are never any deletes.
With monitoring turned on for the table you can read which partitions/subpartitions have changed from the user_tab_modifications view and base the partition list on that, or alternatively use the gather stale option of DBMS_STATS to do that for you.
If you have queries that do not use partition pruning then you'll want to keep your global stats reasonably surrent also
If your partitions are named using something based off of a date or sequence, then you can target your "active" partition as long as the partition name follows a standard naming convention. For example, if you use "some_table_part_MMYY" as the name, then the current month/current partition is ID'd by getting the MMYY part out of sysdate.