If you want to carry a firearm that is your choice
Okay' let's begin with your first item, you'll want to carry some medical supplies such as alcohol or alcohol swabs. This is ideal for cleansing wounds or scratches that you don't want to get infected. Infection is very bad and will ruin your days to come. You also want some gauze or bandages, simple Band-Aids, butterfly Band-Aids and it wouldn't hurt to have an ace bandage. You should also have a small tube of an antibiotic ointment, for example Neosporin. This is great for after you have cleaned your wound with the alcohol and prior to bandaging it. Another thing to carry that could become an asset is a small bottle of aspirin. This is where it gets a little rough for some people. Go buy a suture. Some people may have a problem with sewing their own body and in some cases it's very necessary, but highly unlikely if your car breaks down in the middle of nowhere and you might have a day and a half hike to get to civilization. However if you're interested in a suture you can find them and a medical supply store and usually will not have to have a license to buy them. Now keep in mind, I would recommend just buying a pre-made survival kit but you could piece one together yourself with only the necessities if you so desire.
Okay moving on. You will of course want some sort of compass, any compass will do, and partnered up with the map that you should keep in your glove box it's a huge help. Waterproof matches or a fire starter will also be useful in case you have to stay the night outdoors or need to cook something over a fire. Now this leads me to a point that may help you. If you don't have papers to start your fire, go to a tree that has a nice thick bark, pull off a piece or two, you'll notice that on the inside of the bark there will be pieces that you can either shave off with your survival knife or pull off with your fingers. This will help you start a nice warm fire for you and your family, or just you alone. Notice that I said 'shave',this leads us to the next tool which is a knife. Now you don't have to be Rambo, just have one big enough to do the simple chores of cutting things such as cloth, bandages, rope etc.
Just make sure you have one or some sort of cutting tool. Always carry a flashlight and a pack of fresh unopened batteries, that way you will know that they have a good lifespan. Another recommendation is a thermal blanket, this is highly useful and you can even use it to help build you an overnight lean-to shelter. Now to be on the safe side I personally recommend a jug of water in your trunk. I say trunk because studies show that plastic in direct sunlight releases toxins into the liquid within the container. Another option is to just purchase a water purifier, they're very inexpensive and small enough to fit into your pocket, but in the unfortunate event that there is no water around to use it you better off having a jug of water in your trunk.
In short my friends there are many levels of survival, survival kits and survival readiness. Just be prepared. That teamed with a good mental attitude is necessary and highly recommended for success. The tools and items I listed above may not seem like much but makes a huge difference when you have.