How should I go about installing a 12 volt DC residential circuit?
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.