You want to store something that doesn't change all the time (or twice a year). The time zone database https://en.wikipedia.org/wiki/List_of_tz_database_time_zones is exactly the right thing. So you just store two letters.
From this database you can enquire the time offset, and when daylight savings time is active. It is not just the time offset, it also gives you an area, so many places at the same latitude will have different codes and can individually change their time zone rules, and your software will be able to handle it.
The only time when you need to make changes in your database is when a location changes which timezone it belongs to, which would be very rare.