For any kind of bug out setup - I hate the term SHTF because of ambiguity and social connotation - you have to start with anticipated duration. If you're talking about up to a week then things like water filtration, winter-proof shelters, hunting and trapping tools, etc. aren't important. You're looking at the rule of threes and that's about it. 3 minutes without oxygen shouldn't be a worry outside of safety issues like not running an overloaded rig that has a propensity for failures or rolling over in an accident. 3 hours without shelter means a decent tent and blankets and clothes, maybe with emergency backup plans. 3 days without water means you carry a few jerry cans - 1 gallon (or about 9 pounds) per person per day. 3 weeks without food means you're not worried about it since you'll only be out for a week until emergency services start rolling out and providing water and MREs. It's easy enough to bring some food in spare spaces, but it's not a priority like water would be. It doesn't take much to keep the headaches away, even if you'll still feel hungry. Don't really need to worry about sanitation beyond not ****ting where you eat (literally and figuratively - 100 yards away for catholes, and wash your hands often!) and not eating where you sleep unless you like coyotes and bears and racoons.
Staying out for a month means that your concerns grow. You need to think about decent campsites that wont flood, wind stability, etc. but not significant changes like summer vs snow. It'd be tough to pack enough water though at ~300 pounds per person for a month), so now you're looking at ways to refill your tanks - collection, purification, avoiding storage contamination, etc. Skimming from a lake will require more treatment than a stream, which needs more than a spring, but you can probably trust a proper well after flushing it out. This is the kind of thing where have a 10,000 liter filter can mean a lot vs a cheap 250L filter. Food becomes a concern, but it's easy enough to pack enough rations to get you by for a month, again allowing for a grumbling belly but keeping the headache away. Security becomes an issue here - as the saying goes, society is only ever 48 hours away from riots once the grocery stores are empty. After that happens you'll have people start wandering around looking for other people's stocks and such. Hiding is the primary option here, going far enough out (and hiding your tracks enough) that someone will be disinclined to think that the distance is worth the low odds of someone being out there with enough stuff to make the conflict worthwhile. Having a backup for visitors that do find your camp is up to you.
Staying out for longer means things like planning for seasonal changes in weather and shelter demands, water availability, using wood or solar electricity for fuel rather than propane or diesel, hunting and trapping and preservation of meat, foraging for vegetables and fruit, etc. Basically, every part of living off-the-grid but without investing in comfort stuff. This is pretty much out of bounds for any kind of bug out situation unless you've already got a place staged, your cabin in the woods so to say. Carrying enough stuff to survive for more than a month away from civilization means a medium duty truck at least - loading up your F250 with all of this means you'll probably break a spring getting to your cabin, assuming you don't cause an accident on the road en route.
So, it all starts from duration. I figure that any reasonable risks are roughly a week in length:
A wildfire rolls through the area and burns my house?
A squirrel manages to take out the one transformer that's able to supply the city?
Riots break out downtown after the cops shoot a dude?
I've got 20 gallons of water stored that I rotate through for drinking and cooking for two people, enough dehydrated meals in the cabinet to last a week, a portable battery pack and a couple of solar panels to recharge cell phones or power radios, flashlights that can last for weeks with reasonable use on batteries that are recharged once in a while, a double sleeping bag rated to 15°F, a wood-fired portable grill to backup the propane stove, etc. All of that fits into a couple of weatherproof bins for the back of my truck, underneath the RTT. The truck has a 36 gallon tank and we never let it drop below half, so we can drive 300 miles on a moments notice if need be. Odds are that my wife and I can find a friend's bedroom to sleep in, but we can camp out for a week without issue. A month would be a challenge without a water filter, but that's next on the list. Practice is extremely important.