Your first question is about generators. Diesel is the only way to go. Most gas-powered generators operate at 3600 RPM. While diesel units are usually designed for 1800 RPM On that difference alone it is a no brainer. The slower the machine operates the longer it will last.
Then look at vehicle life expectancy. It should really tell the tale. Even with the newest engines you are looking at 50, 100 or maybe 150 thousand miles before requiring a major overhaul. Also there are the time and cost of frequent tune-ups. The typical long haul truck is powered by a diesel engine. Other than oil and filter changes a million miles is more the rule rather than the exception. And face it those engines get used harder than your daily driver. So for long lasting reliability look at a diesel generator.
Because your place is heated with natural gas you might be tempted or talked into going that route to supply your power. The simplest answer is no. The natural gas generators use a modified gasoline engine. It will have the same deficits plus a few more. Part of it is you are dealing with a pressurized gas rather than a liquid. The tolerances have to be tighter and it needs to be a sealed system. In internal combustion engines the fuel can act as a lubricant. This is very good in a diesel, poor in a gas engine and almost nonexistent in a natural gas system. So which do you think will give you less problems and last longer.
There is an area where diesels have a greater problem. That is when the temperature starts to drop diesel starts getting the consistency of Jell-O. It tends not to flow well under those conditions. In your area a method will need to be planed to over come this.
Definitely forget those tiny portable generators. They are only meant for temporary and intermittent operation. They simply won’t last for your intended planning.
All generators regardless of the type you chose make a heck of a racket when in use. This would eventually drive you crazy. Not to mention the probability of drawing unwanted attention in a disaster situation. So it might be wise to look into ways of quieting things down. You will not make it completely silent but there are ways to improve the situation. The easiest way is to bury it. That is not quite as drastic as it sounds on the surface. What you do is build an underground bunker to house the generator and its fuel tank. Not only will this greatly reduce the noise but also it will help keep the fuel warm.
There is at least one book out there that describes exactly how this is done in fine detail. Essentially you dig a hole. Starting here you have a series of choice whether to use sweat equity or throw cash at it. A professional can do this, you can rent a backhoe or the like or there is the old pick and shovel method. It is the cheapest method yet takes a lot of time and heavy labor.
Once you have the hole you need to pour a slab for a floor. You set up forms to shape it and then decide if you want rebar or not. You can have ready mix trucked in. It is purchased by the yard usually with a minimum amount required. You can rent a small batch mixer for a day or so and go the DIY route. Yes, cement can be mixed by hand in a trough or bucket. This can work for very small jobs but is a bit much for something like this.
Next come the walls. I have seen them done using railroad or landscaping ties. Building block walls is probably better. You can roof it over with wooden planks. Use pre-cast concrete planks. Install steel girders and pour a lid. You talked about the possibility of building an outdoor storage shed. It could be built on top of the bunker to conceal it. Its floor would be the roof with an access hatch.
Because the engine needs air to run and for cooling flow you will need of provide provisions for air vents. These can be baffled and filtered to supply the needed air yet contain the sound.
Along with the generator and its fuel you might want to provide extra space for an eventual battery bank. For efficient fuel usage you will only want to run the generator a couple of hours daily to directly supply the large loads when needed. During these run times you can charge the battery bank. Then you can supply the minimal loads such as lighting and the like from the battery during the off times. For most efficient use you can install a 12-volt system in your home. Along with this you can use LED lighting, which use much less power. Also there are 12-volt appliances available from sources that supply RV needs.
WATER
During the winter if you have your tank in an unheated outdoor shed. You will either need to drain it or have an 1800-gallon brick and a possible busted tank. As for other storage methods we’ll start small and grow. First you have 2 liter soda bottles that can be stored almost anywhere. There are 5-gallon jerry cans to concider. They supply more storage but a little harder to store and hide. Then there are 30 and 55-gallon water storage drums available. They can be either plastic or metal food grade drums. You can line the basement walls and build shelves over them. Then hang curtains or false cabinet fronts to hide them. Or build racks along a single wall. Stack the barrels floor to ceiling. Again you can either use curtains or a false wall to hide them. With these you will need some sort of dolly to move them around. This can also come in handy if you needed to travel those couple of blocks to get water from the lake. Which also implies the needed for some sort of filter or purification method or maybe more appropriately more than one method. Then you can consider building a cistern. Which could be your tank or a concrete tank. Again an underground system, it uses earth tempering to keep above freezing. By no means store your water in the generator bunker. The fuel can contaminate your water supply. Even storing water in a garage need fuel stocks can cause contamination. Along with a cistern system there are systems that collect rainwater from the roof to think about.
You didn’t say whether your fireplace is run from natural gas or if it has provisions to burn wood. If not you might think about those outdoor wood burning home heating and water heating systems.
As for food acquisition you have fishing gear. Have you thought about laying in a supply of traps for land critters?
Have you thought about getting a pop up camper or utility trailer to match your jeep? If you do have to leave either would allow you to pack more than the jeep would hold. If space is limited for storage there are small utility trailers that fold and can be stored along a garage wall. Such a utility trailer can be very useful to haul supplies and equipment for any building projects you are thinking about. Along with any other hauling chores you can think of.
Yes not all of these are the cheapest things. But they are things to think about. They may give you other ideas or lines to think along.
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When in danger or in doubt
run in circles scream and shout
RAH
And always remember TANSTAAFL