You might want to read this:
Should I use field 'datetime' or 'timestamp'?
For example, if you have mysql populate the log record's date/time (using "DEFAULT CURRENT_TIMESTAMP" in your field definition), you will want to use timestamp. For certain situations where you fill a date value from your application, you may wish to use datetime. Be careful with timezones.
Here are the date functions in mysql:
https://dev.mysql.com/doc/refman/5.7/en/date-and-time-functions.html
DATEDIFF(), for example, will calculate the number of days between two datetimes. If you use unix timestamps, you can use standard arithmetic between the values to find the number of seconds between them, and then calculate minutes, hours, days, etc. by dividing appropriately.
This answer is focused on how to handle the dates in mysql. Not enough info to provide guidance on java.