[Clinto]

Mainly we use TriggerHandler to manage events like before update , before insert, etc . write one more class called TriggerHelper , in this classs we write methods to implement logic like when one field is updated do this do that, etc .
The important point in writing all these classes is to keep one trigger for one object and avoid conditions like recursive calls etc.

[Clinto]

We can do things in Apex using Two ways
1. synchronous
2. asynchronous
if your answer is synchronous then go with Trigger, we can invoke a trigger after insert, after the update , before insert, before the update , etc