Prop Balancing Question

Past couple of flights, found a screw that was loose on the spinner and
actually lost one in flight. A&P replaced them, and said during preflight,
check them. If they work their way loose again, need to get the prop
balanced.

Logs show no maintenance on the prop, so I am sure it's well overdue as it
has 2400 hours on it.

Today's flight, lost a screw in flight, and talked with my A&P. He is
going to arrange for a person to come out and balance the prop tomorrow.

Question is, after the balancing is done, what should I look for (if
anything) other then unusual vibrations and the like?

Is this one of those types of repairs, where I should stay in the pattern,
or is it OK to go to the practice area?

Plane is a 1976 Beech Sundowner.

Allen