With your bug out bag you might also want weapons for apocalyptic survival. So what gun do you need? That's actually pretty tricky because everyone has their preferences. I can give some advice for what works for me, but in the end you have to decide for yourself what you want.
1. Know your limit. A lot of people want to feel like a badass so they carry .50 AE desert eagles. It's ok if you can't handle that much power though. They have heavy recoil and are a bulky handgun. .45 is a popular and common pistol cartridge. Even that might be too strong. 9mm is good too. 9mm is often criticized for being weak. Some maniac all hopped up on PCP can survive them and kill you! Well that's kinda the hype. Truth is shot placement is important. If you can hit vital areas you can still stop them. 9mm is pretty decent at knocking a person down. Even .22 would work in a bind. I wouldn't suggest .22 for self defense, but maybe for hunting. Anyway where I'm going with all of this is to let you know not to feel like a wimp if you can't handle the powerful handguns.
2. Don't carry too much. In the video games you can carry a pistol, a shotgun, a machine gun, a shotgun, a rocket launcher, a plasma rifle, a plasma cannon, and a chainsaw. That doesn't work in real life. If you're just looking for self defense at home or you're in a survival situation living out of your car you can hold a lot more weapons. If you're on foot with your bug out bag you need to pretty well figure out what you really need. It's pretty tough to carry a Marlin 336, an AR-15, and a Mossberg 500 all at once.
I would bring one handgun in the kit as a bare minimum. Even if you don't want a long arm a pistol is good to have. It's light and relatively compact. If you are bringing long arms such as a rifle or shotgun I would suggest only bringing one.
3. Have some idea what you want out of a gun. If you want defense from the evil zombie hordes an AR-15 is an excellent battle rifle as the ammo is light and you get a good ammo capacity. If you want a versatile weapon shotguns can be loaded with just about anything your imagination can think of. Bird shot (tiny lead pellets) can make a painful defense round with less likeliness to kill the target if you really don't feel like ending a human life. It can also be used for bird hunting. Slugs (giant chunks of lead) can be quite effective in hunting or lethal self defense. 12 gauge LTL (less than lethal) rounds including taser and sandbags are available. 12 gauge signal flares are available if you get lost. If you want a harder hitting rifle for hunting a good hunting rifle is a good way to go.
If you want the versatility of having several types of weapons available having another person come with you might be a good idea. The buddy system is just a good idea to have anyway, but this is just an extra perk. You can have a bolt action rifle for hunting large game, your buddy can have a shotgun for the jack of all trades use, and someone else can have the AR-15 or whatever semi auto weapon for combat.
4. Keep ammo in mind. Some types of ammo are heavier than others. .22lr is extremely light so you can carry a lot of it and for small game it's a pretty good round. .50 bmg is super heavy, expensive, and pretty overpowered for hunting. It's good to be able to carry a good quantity of ammo especially if you have to rely on it for a while.
5. Keep your weapons secured. I don't keep weapons with my bug out bag. I keep the bag in my truck. If someone breaks into my truck and steals my gear I'm upset but I get over it. If they steal one of my guns from my truck then I just armed a criminal out of negligence. That's just how I view it. I highly recommend keeping them secure. How you do it is up to you.
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