Yep, it's gotten to the point where I think I need a gun here at the house if this violence within the US continues. Even though I live in the country and feel relatively safe, it takes the police longer to reach us as opposed to where I used to live and I don't trust my neighbors to protect me like my previous neighbors in the burbs.
So what kind of gun is best for a first time buyer? There is a shooting range 20 minutes from home that's probably open.
My thoughts, based on limited experience so take it for what it's worth.
You'll need to consider the physical size of the gun given your size how you would plan to carry it. If you want to carry it in a small handbag you'll need a small gun. If you have small hands you'll want a small gun. I have quite big hands and many of the "compact" options feel like toys so I prefer something a bit meatier. If you're planning on concealed carry check the laws regarding permits where you live and figure what size firearm you can carry concealed on your body. Here you'll also need to consider the way you routinely dress - if you typically wear tight-fitting clothes you'll struggle with concealed carry but if you often wear flowing or loose-fitting things you can carry something larger.
Consider the caliber of ammunition you'll want to use, thinking about recoil and how well you'll deal with recoil. Obviously a .45ACP will kick a lot harder than a .22 but will also do more damage when it arrives. Then there's the cost of ammunition to consider - larger caliber ammunition is more expensive.
A semiautomatic handgun will hold more rounds than a revolver. Depending on the caliber and the overall size of the gun you could be talking anything from 5-6 rounds to 17 rounds in the magazine.
For home defense you may want to consider a pump action shotgun or a semiautomatic rifle. In many ways rifles are better for home defense than handguns simply because they have more points of contact with the body and are therefore easier to hold steady. If you're strong enough, and your rifle is robust enough, it can also be used as a club if you run out of ammo and don't have time to reload it.
Where home defense is concerned you'll want to give some thought to where a bullet goes if you do ever have to fire at someone or something. Consider where you can take a stand in your house, thinking about being able to hold an area without destroying vital elements if you do have to use force - for example, you don't want to find that shooting an intruder means that any bullets that miss (or that pass through the intruder) end up trashing your oil tanks or your furnace or something. Depending on who lives in your house with you, you'll want to make sure everybody is gathered together so your family aren't harmed by stray bullets, or mistaken for intruders.
Your best bet is probably to go and talk to a local gun shop, handle a few guns and see what feels comfortable for you. If your local range has an option to try guns so you can get a feel for how they actually fire, recoil etc that would be even better.
Unless you really have no option, don't bother with the places that have trigger locks in everything and refuse to remove them. It's really hard to get a feel for the gun if you can't put your finger on the trigger.
Of course you'll also want to consider the price. If you're talking something that you're not expecting to ever actually use but just want a sense of security, you won't want to spend $1000+ on a top-end firearm.