"Give your best" vs. "give of your best"
Give your best
give one's best
perform a task as well as possible; "The cast gives full measure every night"
"Give of your best", implies not only effort, but everything, so I would just use "give your best", when specifically referring to the one thing, effort.
One would usually say :
give your best.
"Give of your best" has the implication of giving all about yourself that's the best. For example, there is a hymn that goes "Give of your best to the Master", and goes on to tell about your strength, and your youth, and your intelligence, etc.