I am just curious how much time and effort I should put into some of this or if I should just "put my faith in Microsoft" and that DTA knows what's best.

The DTA does not always know best. I've found that it tends to go overboard.

When I use it (which isn't often) what I'll generally do is implement its suggestions 1 by 1 and test the performance improvement, then I implement the ones that have the most impact.