There are three areas that I think are a good start: 1. food storage, preparation and self provisioning 2. Water purification 3. Basic first aid. The issue of food can be as simple as understanding how to maintain a balanced diet with easily stored foods or as complicated as how to provide all of your nutritional needs in a given environment (Urban, Rural etc.). Water purification is also critical, and while boiling is always a good solution, understanding other means of water purification is important. Finally a basic Red Cross first aid class is a great way to start learning the skills to deal with all the things that can and will go wrong with our bodies.
1. Any Pump Shotgun (Mossberg 500, Remington 870 etc) 2. A Reliable rifle in 30.06 or 308 3. 22.LR Revolver Shotguns can do just about anything you need them to out to 100 yards due to the versatility of different cartridges. You can carry rifled slugs, buckshot, 8 shot, 4 shot and T shot at the same time and be able to take down any game you encounter and deal with most defensive situations. Shotguns also have the advantage of being more user friendly than other firearms. It is easier to hit a rabbit with a shotgun than a .22. A scoped bolt action rifle gives you range and power if you need it, and if you practice regularly 8 inch groups at 500 yards should be no problem. Pistols have limited utility, but the 22lr is an easy round to find and carry, and can be used for food acquisition and limited defense. In most scenarios, firearms will be primarily for getting meat and defensive situations, and the above will do fine. Even urban areas tend to be full of pigeons, rabbits and squirrels, so its important not to discount the utility of hunting weapons. I`m not a huge fan of AR variants, as the 5.56 x 45 mm is not that useful in the woods, and any situation in which you are alone and need to engage in an extended fire fight necessitating multiple 30 round clips is probably going to end badly for you.
Another thing to think about is building skill sets. Equipment can be important, but its hard to predict exactly what will happen and where you will be when it happens. Can you read a paper map, cook with fire, purify water or deal with a bad cut? The more you know how to do, the more confident you will feel in an emergency situation and be better able to improvise where necessary. It could be worthwhile to make a list of skills you would like to learn and work towards learning them.