For your purposes I like the Beretta 92FS/92A1.
It's a very aesthetically attractive gun, making it more appealing to girls (I promise I'm not making this up as stupid as it sounds. I've taken girls shooting with friends who were bored with my friends' Glock and XD type guns but ooohed and aahhhed at my Beretta).
It's a very friendly gun. Low recoil, easy to handle.
It's a very reliable gun.
It has a heavy first trigger pull and a manual safety to ease her mind.
I'd grab a 92A1, a GunVault safe for it, a Streamlight TLR-1 to fix to the rail, and fill a few magazines with a quality load like Federal HST 147-grain. After all, if you only get one, go full-out.
Actually...if you really only get one...you might go look into a Sig Sauer P226 or HK P2000. Something that can last bulletproof for ages.
Beretta PX4 .40 S&W - Beretta 92FS 9x19 Para - Rock Island Armory GI 1911 .45 ACP - Colt 1968 Detective Special .38 Spc. - Ruger LCP .380 ACP - Daniel Defense M4V1 Carbine 5.56x45 - Alpine Industries M1 Carbine .30 - Steyr-Mannlicher M1895 8x56 - Ruger 10/22 .22LR - Remington 870 Express Tactical 12GA - 1943 Izhevsk Mosin-Nagant M91/30 7.62x54R