Changing these will impact how often the table is analyzed based on the rough count of changed rows. You may want to adjust autovacuum settings as well so that dead space can be reused.
default_statistics_target
Increasing this from default 100 will result in longer planning time, but you may get a better plan (more consistently).
What is the best option to ensure that the table statistics stay upto data and that the best Query Plan is generated.One option would be to use CRON and regenerate the table statistics every 15 minutes, or disable auto vacuum ANALYZE function, but neither of these options feel write.
You can check if autovacuum is working on this table by checking pg_stat_user_tables or turning on logging of autovacuum and reviewing your logs.
How does the auto vacuum analyze function work? Does it
use a subset of the whole table to regenerate the table statistics
Yes. It scans 300*default_statistics_target rows and for each column estimates null fraction, most common values and the frequency of those, histogram_bounds and other info found in pg_stats.