You generally dont need to over complicate things unless you need to.

1) Stats will kept up to date in most cases without your needing to worry about it. There is an automatic job that detects those tables that need refreshed stats. If you perform large adhoc maintenance, then you might want to consider a manual call after that operation.

2) You dont need dbms_redefinition for after purging. You *might* not need to do anything (because we will re-use free space as required). You *might* be doing an 'alter table move' or 'alter table shrink space' after the purge, in which case, you might follow that up with a dbms_stats call (see 1)

3) With dbms_stats, I always recommend going with the defaults *unless* there is a reason not to. 'for all columns size auto' basically means the database will actively monitor queries in the database, and try make an intelligent decision based on your queries about which columns will need histograms and what size those histograms should be.

Some people find its a bit "generous" with histograms, in which case, you can set a table level preference to explicitly limit or exclude histograms if its causing your problems.

The METHOD_OPT options are all in the docs

http://docs.oracle.com/database/121/ARPLS/d_stats.htm#ARPLS68582