Defense In Depth is currently renting the perfect firearm for people new to shooting. The Smith & Wesson M&P 380 Shield EZ may have an overly complicated name, but it was specifically designed for people who find the strength and grip necessary to operate most handguns intimidating. (The "EZ" stands for "Easy".) It is light, easy to manipulate, easily to conceal, and inexpensive.
There are plenty of reviews online, almost all of them glowing, so you don't have to take our word for it. Here's Kelly Pidgeon from Armed & Feminine talking it up:
This gun is manageable by almost anyone, and is perfect for introducing your loved ones to shooting. We rent this firearm - like all our pistols - for $14.99. We also sell it in-store, so you can try it out and walk out with one in the same day.
For gun guys who worry about the defensive efficacy of the .380 cartridge for your family and friends, we encourage you to take a look at some of the great modern defensive loads available in .380. Here's a video of some Lehigh / Underwood loads managing more than 24 inches of gel block penetration after passing through sheet metal — more than double the FBI standard of 12".