Do I count the barbell as well as the plates ? How do I find out what my bar weighs ?

Yes, you are lifting the barbell, too, so it counts. Different types of bars will have different weights, but generally, a standard Olympic bar will be 45 lbs. and an E-Z bar can be anywhere from 25-35 lbs. If you're not sure, ask a trainer, search online by your brand name, or weigh it for yourself.