I know this is an old thread, but since it popped up again...
I am an NRA Certified Instructor for pistol, rifle, and personal protection. Depending on the class, we usually have between 40-60% of participants being women, and about half of them have not shot a firearm of any kind. The average class costs $100-$150. We charge $40, and includes ammunition.
The best thing that a "newbie" can do is to take the NRA Basic Pistol Course before deciding what handgun you want to buy. Several of my students come with a gun that they were "sold" and decide after the class that they would much rather have something else. We have around 30 handguns at any given class and the students end up trying about 4 of them, and most poeple have said after the class they actually prefer something different that they thought they would at the beginning of class. When you are spending several hundred dollars on a quality handgun, it pays to make the right decision the first time.
Unfortunately many women are steered right into a snub-nose, lightweight, .38 Special revolver, which frankly is not an easy gun to shoot for a beginner. However, if you can master that, everything else is cake. The most important thing though, whatever your choice, is to continue practicing, and practicing.
What kind of gun should I get? That is impossible to answer here, but a good rule of thumb is to shoot most powerful cartridge you can do comfortably, consistently and accurately. Here is something I put together to help answer that question:
http://www.danvilleconservationclub.org/whatgun.pdfShotgun, rifle, or handgun? For carry on the person, the choice is almost always going to be a handgun. For home defense the handgun works very well, but whatever your choice you will need practice to be proficient. A handgun is going to be less effective at stopping an attacker than a rifle or shotgun. While camping, in a trailer, a long gun (shotgun or rifle) is going to be very unwieldy because of its length.
A "pistol caliber carbine" (a "carbine", pronounced "CAR-bean", is a rifle with a somewhat shorter barrel, 16-18" usually) is a very good choice for home defense, it will also (generally) be lighter, and will have much less recoil that a rifle or shotgun. A "pistol caliber carbine" is designed to shoot handgun ammunition. It has an advantage over a handgun because it will be more accurate, and has a small power advantage over a handgun. The next step up from a "pistol caliber carbine" is the M1 .30 Carbine (a.k.a. US Carbine, Caliber .30, M1). If there is a "funner" gun to shoot I'll eat it. It's light and has very little recoil. The next step up from there is a semi-auto .223/5.56 rifle. The recoil is still low but the noise from the report goes way up.
A lot of people recommend a shotgun as the "best" home defense option. Most 12 gauge shotguns don't fit women very well, and 12GA recoils more than is comfortable. A
"youth" model 20 gauge shotgun is the best choice for most women. Even then, a shotgun can be quite heavy, my little (yet full grown) niece who is 5'2" and 110# soaking wet has a tendency to lean back to counterbalance the weight of a shotgun, not good. "Reduced recoil" buckshot loads are available for 12GA shotguns and the recoil is about the same as a 20GA, and an adjustable stock can make it usable for more than one size person -- some types even have recoil reducing contraptions built in.
The OP also mentioned "critter control" and it's hard to beat a little .22 rifle for that purpose.
As far as safety and the kids at home, that is covered in the class as well. Kids, like adults, need to learn firearm safety. And since adults are responsible for their kids, including criminal liability in most states for their children's misuse of guns, it pays to know your options. Store guns and ammo separately. Store them so that the are not accessible to unauthorized persons (kids and adults). Proper storage limits your liability. Remember that the lock is only as secure as the key and that no storage method will prevent a determined person with enough time and tools from accessing your valuables. A child in your home has a very long time - literally years - to find your hiding places. Out of sight out of mind is one thing, but don't fool yourself into thinking that you can "hide" your gun.