What you're describing is basically what you'll find in an RV. However, it's not likely to be as useful as you might wish.
The "12V" in the name of a lead-acid battery is nominal. The actual voltage might vary between 10V and 15V. Most electronics can't tolerate that kind of variation. Audio components can suffer from ground loops. Even though many devices in our homes run on DC today, AC is still a good choice for power distribution.
In an RV, most of the 12V goes to lighting and fan motors, which simply get brighter/darker or faster/slower, within that range of voltage. The variation may not be ideal, but it still works.
Since your voltage is 1/10th that of conventional house wiring, your current will be 10x as much. That means the conductors will need to be much thicker - more copper, and more expensive.
Once you have both 120VAC and 12VCD in your house, it's annoying to switch back and forth between 120VAC and 12VDC. Whatever you set up, consider a 12V converter for when you have shore/grid power, so your 12VDC devices can be used all the time.
A widely-used standard for DC outlets is the "cigarette lighter" plug. If you install them in your walls, I recommend labeling each one with the max current.
Be sure to put fuses on each circuit, at your distribution block. And a master fuse as close to the battery as possible.
When a lead-acid battery charges, it releases hydrogen gas. If you're going to put that system indoors, you need ventilation to clear the gas, and prevent an explosion. Alternately, you can use sealed lead-acid batteries ("SLA"), but they're more expensive.
Be very careful to keep your two wiring systems separate. Don't ever run them in the same conduit or junction box. Labels on the low-voltage will help avoid mixups in the future.
The cheapest, simplest, most reliable way to provide emergency backup power to a home is a generator with a transfer switch. Even RVs with batteries and solar panels will have a generator.
Note that these days the best answer for solar, if you aren't determined to go completely off-grid and if your electric company supports it, may be to get inverters that support line synchronization and ask the electric company to set you up for net metering.
In this setup the inverters and line feed the house in parallel. If you're producing less power than you need, you buy the remainder from the power company; if you're producing more than you need, you sell the excess back to the power company. Much simpler than trying to maintain local batteries for extra or nighttime power, ensures that all power generated deducts from your electric costs, and in some cases you may be able to sell carbon-reduction credits as well.
I've been quite happy with this setup. I have a relatively small solar setup (8 "standard" panels), but my electricity use is relatively low too, and in the summer I usually do have one or two months of negative net usage. I haven't yet gone negative enough to actually have a negative bill, due to the utility's $6 account fee, but I've come close.
Note: The one disadvantage of a newer metering system is that, to keep your system from electrocuting linemen who expected a cable to be unpowered, net-metering systems are designed explicitly not to run in "island mode"; if the network goes dead, they shut down for safety. That does mean you have to make other plans for dealing with blackouts. As I said, if being able to go completely off-grid is important to you this may not be the best solution.
If it sounds interesting, ask your solar supplier/contractor for details. Anyone competent should be able to explain it in detail, and run numbers to tell you how long it would take for the system to pay back it's purchase cost after figuring in any currently available rebates and carbon credits (though the latter will be a best-guess, since these are sold via an auction mechanism and prices may change depending on supply and demand).
Best Answer
Drew there are panels that will do exactly what you want. They use the existing wiring and have a limited number of circuits. These manual transfer of 1/2 dozen or more circuits is really expensive. See generac, reliance 6 circuit transfer switches. These systems cost in the range of 350.00-450.00 I have seen them used with a 2kw generator.
Old school lightbulbs that is 200 not just 1. The house I am thinking of ran there gas furnace. Lighting they needed and refrigerator. When they wanted to run the well they turned off the refrigerator circuit and turned on the well pump.
So it can be done even using your existing wiring. I would suggest a generator interlock kit this locks out your main breaker while turning on the breaker to feed the home from another source whatever it is. You turn off all the circuit breakers you don’t need or cannot power with the new source. A lot cheaper and works similarly for under 100$.