Yes, put transformer on a NORMAL 15 amp breaker.
Yes, only drawing about 3 amps at 110v
As to the cost, if you were to leave 300 watts of lights on 24 hrs a day, day in, day out, it would consume about 216 killowatt-hours of power over a months time. This would cost you about $17 a month based on 8 cents per killowatt-hour electricity cost.
Dodgeman