I started going shooting with my wife shortly after we started dating, way back in high school. She had never shot before, but she knew that a good part of my time was spent in the woods, so she came along right from the start.
She's got her own rifles and pistols, and I don't have too much to say about what she chooses, as long as she doesn't try to nab something out of my half of the gun safe. It has helped to cut gun stocks down to fit her, as it's been tough to find left-handed "youth" stocks ready-made. Although not very sensitive to recoil (her favorite rifle used to be a 444 with 310 grain reloads), she does prefer to be kicked less rather than more, and she's settled on a lefty 7-08 as her main hunting gun. She's also fond of the 260 Remington, but that's tough to find in left handed rifles. She doesn't like minor power hand guns, oddly enough. Although she shoots them well, she'd rather see the target go flying instead of just punching holes in it. She hasn't hunted with a handgun yet, and probably won't until after she gets the archery bug out of her system a little.
My daughter's only 4, but she's been coming on hunts since I had to put her in a back pack to bring her along. I also have a sister, a grandma, and a step-grandma that have been big fans of hunting. My sister was lucky enough to draw a coveted cow tag for her very first rifle elk hunt, and she connected on a very tasty antlerless elk. She also shoots left handed, but prefers long action rifles, so she's easier to find rifles for. She took her elk with a Remington 700 in 7mm Remington Magnum. She doesn't cut her stocks down, and she doesn't really need to (she's about 5' 8" or 5' 9", maybe). For those folks that might think they have a daughter that will never want to go hunting, my sister was very much against hunting until she was in her twenties, so there's still hope!