MOVE
seriously, tell them they need to GTFO, there are too many nice, safe neighborhoods around Columbus to have to worry about shit like that. Of course, this is assuming they are in an apartment and moving is reasonably easy.
If for whatever reason they can't move, a dog is a great deterrence. Rottweilers are very loyal and very protective.
If they are dead set on just getting a gun, so be it. But make them practice with it, and get at least a small amount of training.
Shotguns are large and have a good bit of recoil, which can be a problem for smaller women. The other thing is that contrary to popular belief, they do indeed need to be aimed.
Handgun would be easier to use. Get something that's fullsize and has night sights, or invest in a good flashlight.
My suggestions for around or under $500 (new or used, look around)
1911
-Rock Island (I love mine)
-Springfield GI
-Charles Daly
Springfield XD
Bersa Thunder
Ruger P-Series (a bit chunky for my taste, but cheap and reliable)
These are all semi-auto guns. If they decide they prefer revolvers, check out S&W and Taurus. Their best bet though would be to go to Blackwing, talk to Greg to see what they have in the price range, then rent them to try them out and see what they like.