My hosting company does not support SUPER privilege - can I use CiviCRM with them?
There are only two scenarios in which CiviCRM requires the SUPER privilege:


You're using a very old version of MySQL.  Versions of MySQL 5.1.6 and higher support the TRIGGER permission.  Before that, SUPER was necessary.  MySQL 5.1 reached its "end of life" at the end of 2013.  No modern server should have it installed.
You're attempting to use the advanced logging feature: Administer menu » System Settings » Misc, Logging set to Yes.  If you need this feature, you really need a VPS.


All that said - @Christia is right.  StartLogic is entry-level hosting.  CiviCRM has heftier requirements than entry-level hosting gives you.  Expect poor performance unless you move hosts.