Shotguns hurt my arm.
Okay, this maybe the Ruger LCP I also recommended would be good, but it is a very light weight, small pistol. Another possibility, which is a little larger, but still fairly small and female friendly (my wife's personal weapon and she loves it) is a Sig P232, 7 + 1, in 380 caliber.
You can buy a Marlin model 60 .22 semi-automatic for about $150, brand new. It is easy to shoot, reliable with good ammunition, and it holds 15 rounds. It would be a good start and is so cheap and cheap to shoot that it would serve you until you decide you need something else.
Buy some bulk ammo to play with it, and some velocitors to use for self defense. Shoot at least 500 rounds (about $20 of ammo, bulk) so that you feel comfortable with it and with clearing stoppages. You will always be able to sell it for $100 if you do not like it.
Marlin model 60:
http://reviews.walmart.com/1336/17200691/marlin-model-60-rifle-22-lr-reviews/reviews.htm