How to detect if a trigger is fired for an insert or update?

I need to make a table in my database that has all of the history of all DML statements that occur in a given table. The LOG table is like this:

LOG table has a sequence for auto-incrementing the ID column and TS default is NOW.

Do I need to create a sequence for every statement first or I can just create triggers for AFTER a DML statement is fired?

CREATE TRIGGER UPDATE
  ACTIVE AFTER INSERT OR UPDATE
  ON TableA
AS
BEGIN
  INSERT INTO LOG (event,record)
     SELECT record FROM TableA; # what I need to add here to set the event = UPDATE,INSERT or DELETE?
END

Can I use something like this in my triggers with a statement to add an event values?

To detect the type of event, you can use the INSERTING or UPDATING (or DELETING) context variables.

As an aside, do not use SELECT record FROM TableA in a trigger on TableA, instead use the NEW context (or OLD for a delete).

The solution would look something like this:

insert into LOG (event, record) 
  values (case when :inserting then 'insert' when :updating then 'update' end, new.record);