For a newbie to guns, I'd recommend checking out the resources for women that the National Rifle Association offers
(I'm an NRA member because they are the leading defender of 2nd Amendment freedom. Although -- perhaps because -- I live in the anti-gun capital of the country, I value the 2nd Amendment very highly).
http://www.nrahq.org/women/index.asp
Have you studied the gun laws in your area? For instance, some guns are legal in DC but must conform to certain restrictions (such as ammunition clip capacity, tubular magazine and not bottom-load rifles).
Most of my gun knowledge and experience are from growing up in California and Oregon and shooting my father's, brother's, uncle's and grandfather's handguns and rifles. In DC, I rely on bear spray and a dog because I haven't jumped the myriad hoops to gun ownership here.
For home security I'd recommend a shotgun. Opinions vary (surprise!) but that's mine. You don't have to be as accurate and just the sound of the pumping action could cause an intruder to have to change their underwear. Also, handgun bullets travel further than shotgun pellets so I've always understood that shotguns are safer for the neighborhood.
For auto safety and walking around, I'd be inclined toward a
9mm handgun with as big a clip as your jurisdiction allows. My brother had a Ruger 9mm that I enjoyed shooting. The kick was mild and the gun was comfortable. You should "try some on" for size but you'll have to shoot them to know.
(how are you going to conceal it? Purse? Leg-shoulder or belt holster?)
Have also enjoyed a .38 revolver. Whatever caliber you settle on,
you have some latitude in grips (bigger or smaller).
You also have
choices in ammunition (such as "hollow point" bullets). Larger caliber ammo costs more so factor that into your shopping if you're going to be doing a lot of target practice (which I recommend).
Here's a woman perspective you may want to consider (the merits of a .22):
http://thesurvivalmom.com/2009/12/14/9- ... arry-a-22/
Also, an argument for as large a caliber as you are comfortable with:
http://www.shootingtimes.com/handgun_re ... ed_200811/
And points to consider on concealed carry:
http://www.usconcealedcarry.com/public/1319.cfm?sd=45
If you have no experience shooting, plan on spending a lot of time at a firing range. Firearms training would also be a good investment. The NRA website can point you to some options. If your 15-year old is going to be around the gun, firearm instruction for them would be wise, as well.
If you are going to travel out-of-state with it, be sure you know what the gun laws are where you are traveling. Many people have found out the hard way that their home states' gun freedom is irrelevant when they enter DC.
By the way, the NRA sells some concealed carry accessories - such as purses and holsters that attach to your car seat.
Good luck. You are wise to be seeking counsel.
P.S. Where do you expect to be encountering "critters" and what kind of critters concern you? While you're figuring out the best gun, you could go ahead and buy bear spray from REI. It would protect you from 2-legged and 4-legged predators.
