A 20 gauge is effective at true home defense ranges and is manageable by even a small woman.   A 12 gauge with a muzzle brake, a recoil absorbing stock, or both is manageable for a small woman with some practice.   The "bump in the night" weapon at my house is a 12 gauge Mossberg 500 with a Blackhawk recoil absorbing stock.   My wife can handle it and I have to admit I like it too.