Rifle: Remington Model 7 or Model 700 Youth in .243, .260 or 7mm-08. Savage also makes a very nice youth model.

Shotgun: Remington Model 870 Youth 20 Gauge.

How the rifle/shotgun fits youis important, so assuming you're an average sized 11 year old, a Youth Model is the way to go, and you can always put an adult sized stock on it as you grow.