Electrical Power is intrinsic to our modern quality of life, and it can become a major survival factor depending on ow bad things get. A calorie you don't expend pumping water or grinding or turning or sawing or harvesting is a calorie you don't need to produce as food. Avoiding Injuries by using power tools and lights, could be the difference between making it and snuffing it. Yes, the human race got along fine without electricity for thousands of years, and you could too, but having it is a huge advantage, even if you can only use it sparingly.
Any electricity system will have a generator , optional (Chemical) battery storage, and loads that do work. These loads can be AC (alternating current) or DC (Direct Current) . An Energy conversion is ALWAYS lossy - energy is typically lost as heat.
Ironically, many of our appliances use electricity to produce heat - baseboard heating, electric ranges etc. This is about as wasteful as it gets.. anything that needs to be heated post TEOTWAWKI needs to be heated by burning a fuel directly, be it water, or your home. Make sure your plans do not include electric heaters of any kind unless ther eis no way to avoid them ( say an Aquaponics tank you need to keep at 68 degrees.. even so take steps to reduce that load as much as possible via solar heated water exchange etc. )
You can charge a battery just using a long cable, a rectifier and time. The wire acts as an antenna (AC) and channels that energy to the battery (DC) and then to earth ground. Its slow, but if all you want is emergency power for a short period it could be used.
Solar panels use semiconductors and quantum effects to produce an DC electric current, this will typically be used to charge a Battery - An Inverter will take that DC current and convert it to AC , or you can use only DC loads.
Fuel Cells convert hydrogen to electricity directly. As a technology they have promise, but tend to be more expensive per KW than Solar , and they just aren't a real solution right now IMO. In another 5-10 years... if we get them...
Fueled generators burn a hydrocarbon to rotate a shaft to generate electricity - They can be either AC or DC ( A Welding rig typically does both) They can be used to charge a battery/inverter system , or the power they produce can be used directly . Fuel is typically perceived as gasoline or diesel, but natural gas, propane, alcohol, methane, or wood gas (hydrogen) are also viable - and probably easier to obtain sources.
Gasoline is the worst. Difficult to refine, dangerous to store, and the shelf life, even with stabilizers is poor.
Diesel is a little better than Gas, but not much. Kits are available that allow you to make your own bio-diesel, but this presumes a supply of an oil - the first diesel fuel was peanut oil. That may or may not be practical depending on what is around you and what services are still running. Nearly every tractor out there will be diesel, and you will be stuck with needing some. Its quite common for farms to have large tanks of the stuff, but it will go bad over time.
Kerosene - Easily made, and can be used to run a diesel. This fuel will be available to anyone with oil sale they can heat up - and mixed with engine oil etc, will probably not damage a diesel too badly.
Propane is a great fuel - long shelf life, no one questions large purchases, and you can use it for cooking, running a generator or heating your home. A properly equipped main tank will allow you to fill smaller cylinders for use elsewhere.
Natural Gas - generally delivered via pipeline - requires grid pumps to keep working. Pretty much the cheapest fuel however. Dual Fuel appliances cost a little more, and most gas appliances have "conversion kits" - having a Natural Gas line for normal times and the ability to convert to propane for times that are less normal, will give you some amount of longevity if fuel supplies are sporadic.
UPDATE: If you have a natural gas well, tat is about as good as it gets. Hard to find. Regulations make it hard to keep
Alcohol - This used to be the farmer's fuel of choice (along with kerosene) - Early Fords were designed to use it, and many modern vehicles have a sensor that will allow the vehicle's engine to determine O2 mix. But there is simply less energy in a gallon of Alcohol compared to Gas. Of course any biological matter can be fermented. Some designer bacteria are being developed that may be able to directly convert cellulose to alcohol - but without that you are fermenting sugars. The good news is a stainless steel still is relatively cheap to purchase, and this becomes a potential revenue/trading source in addition to fuel. I have no doubt alcohol will be heavily abused after things go really south. - Further you need to expend energy to distill it , so you main benefit is having it as a liquid fuel vs a solid one ( wood)
Wood Gasifier - There were commonly used in WWII by citizens with no other way to power their vehicles. You basically burn wood really really slowly, distilling a layer of wood on top - this releases hydrogen which can be captured and shoved into a gasoline engine - apparently without ill effects. H2 gas is difficult to collect and store, the system requires a lot of attention , and this is basically a DIY piece of equipment, but a neat option if wood fuel is abundant.
Update: Hyrdo electric - if you have a good water flow on your land, this is an option, but since the EPA has claimed jurisdiction on pretty much every water way - even your little stream is considered navigable now- diverting a stream throug a hydroelectric plant or building a dam is now prosecutable
Update: Wind. Wind doesn't blow all of the time. In order to generate real power you need 20-30 mph winds consistently with current technology, and te turbines need regular maintenance - which means going aloft every 6 months to a year, or lowering the mast to the ground. On a cost to KW -HR solar is a much better choice in almost every circumstance.
SO back to electric power generation.. Solar is expensive, but panels can be expected to last 20 years or so and they are maintenance free. They are bulky and not the easiest things to steal, and they operate near silently ( the Inverter fans make some noise) - Designing an all DC house can remove the inverters and increase efficiency on the order of 20-30% , but DC appliances and bulbs are specialized and more expensive. DC also doesn't carry very far, so in an all DC system the loads should be as close as possible to the batteries and the Panels. In the modern world Photo voltaic solar makes almost ZERO economic sense. You will be lucky to break even under current economic conditions. Post TEOTWAWKI however, I think they will pay for themselves many times over - quiet, dependable power.
Generators are significantly cheaper, but produce a lot more noise, and burn fuel. .which you will constantly need more of.
Many inverters allow the use of BOTH solar power and a generator to charge and run the same set of batteries and power the same loads. Choices are good. Choices are also more expensive.
Under either system batteries can be used, but they add inefficiency as energy is lost in heating the batteries during charging, and again during discharging. However a battery system means you can run silently at night and still enjoy the calorie saving benefits of electric power. With proper sizing batteries can also make up for shortfalls in production ( cloudy days for solar, days you don't dare run a generator or are without fuel) Batteries are of course , stupidly expensive. Deep Cycle lead batteries , golf cart batteries , or specially designed solar Lead cells all have a shelf life. Anywhere from 3 to 20 years. Your best choice is Iron-Nickel batteries - they are near indestructible and last decades. Edison's original batteries are still working fine. . They also take up the most room and weigh a ton.
Some work is being done using super capacitors to store energy, and if that pans out they will replace batteries like these. But like Fuel Cells its all very promising but nothing that has real practical application for the cost as of yet.