I am in a heavily customized Drupal Commerce site where I have 31 Features. Eleven (11) of the features are based purely on off-the-shelf 3rd party Drupal modules, the rest of the Features (20) have dependencies on the other Features already existing and each other. 

I need to update the normal off-the-shelf 3rd party modules (40 of them) and Drupal core (from 7.23 to 7.26).

In the past and on simpler websites, I have updated all of the modules (if non-problematic) then disabled them and updated Drupal core. After updating core I then turn modules on, one at a time, and make sure things are still working together.

I have not used Features extensively like this and do not feel sure about the correct process for updating. 

My impression is that as I update modules, my Features might have some repercussions (do they show up as Overriden?) and that I should, one at a time, Update/Recreate my Features, download the code, upload the Feature to the website and turn it back on.

Is this correct? Should I update all of the off-the-shelf 3rd party Drupal modules first? Then update all of the Features?

Should I update one module at a time, checking for Overrides showing in Features and the updating those Feature(s) one at a time also?

What would the best methodology be in this situation?