The basic paramters that you might want to keep track of are the shared_pool, db_buffers, large_pool and MTS_*. But most of the parameters are static in nature as a result any changes would require bouncing of the instances. But as a DBA you should configure these parameter and make sure that they are sufficient enough for the instance's long run.
If your application is being coded poorly and then if you try to satisfy the application through these parameters, would no way help. On such cases, you would first want to tune the application, before tuning the instance.
Life is a journey, not a destination!