How serious is forgetting my life gain triggered abilities?
Your understanding of the missed triggers is correct. Since the required triggered ability (number 2) is only beneficial to you, there is no penalty for missing it.

The other triggers do not work exactly how you think because they are covered by a slightly different part of the rule than you quoted. The first part of rule 603.5 says:


  Some triggered abilities' effects are optional (they contain "may," as in "At the beginning of your upkeep, you may draw a card"). These abilities go on the stack when they trigger, regardless of whether their controller intends to exercise the ability's option or not. The choice is made when the ability resolves.


Those abilities always go on the stack and they do not have a default choice, so you must make the choice when they resolve. If you do not, it is a missed trigger like any other.