I am going to buck the trend and highly recommend that the very, very first gun for home/family be
Mossberg 500 Super Bantam 20ga OR Remington 870 Youth 20ga
For four important reasons:
1. These guns are very simple to learn to use SAFELY and EFFECTIVELY, more so than ANY handgun or virtually any other type of long gun
2. A 20ga shotgun is EFFECTIVE, more so than virtually any handgun
3. A 20ga youth-size pump gun can be used effectively by virtually anyone over 4'6" tall!
4. Cost to acquire is very low and relatively easy
In my home, we started with a Rem 870 12ga. We will be purchasing a 20ga because the 12ga is just to long and heavy for my 5'6" wife to use comfortably.
LAST but not least, the BONUS:
There are so many fun shotgun sports, out there and accessible, that the barriers to becoming safe, comfortable, and proficient with the 20ga pump gun are about as low as you'll find.
A 20ga youth shotgun can be used at all sorts of trap ranges, gun clubs, etc., usually cheaply and easily, unlike a handgun.