Saving a new item and custom code

I am a bit rusty with the component creator as I haven't used it for a year but I am wondering what may be the easiest / best way to add some custom PHP code that is executed while saving a new item in the joomla backend view.  I have a table I created using the component creator that stores a user profile. Upon saving I have some custom code that I would like to run (in my case it will check with our email campaign tool and see if the user exists, but it could do anything).  Things just get confusing with Joomla's API and JTable, JForm, when you haven't used it for a while.  Are there plugin events that are fired so that I could create a plugin for the OnFormSave?  Or would I have to modifiy the code somewhere in the administrator?  I cannot fine a save function anywhere, so not sure where would be best to modify.

Thanks,
JP

The closest thing I can find to modify may be in the: administrator/my_component_name/tables/mytable.php file which contains functions such as bind(), check(), publish().  There is no save that I see.  Would it be best to just change code in this file perhaps, but which function to use?  I suppose if I do future upgrades I will need to be careful, but I can manage that if I cant do an override and am forced to change 'core' code.