Thanks for posting this. I lived for years in the earthquake zone of southern California, I lost power for a few days in the brushfire zone of southwest Utah, and now I live in tornado alley, central USA, Kansas. I have pondered affordable basic systems.
Once someone wants to build an off-grid system to supply all their needs, I'd go straight to 48V and make the size of the battery and solar panel array expandable...by that I mean...the solar charge controller and inverter should be good-quality units and large enough to satisfy your needs in the future. In the meantime, you can size the battery pack and solar panel array to the minimum necessary to meet only your basic needs, then expand over time.
I had at first wondered about a small 12V system, simply because the initial buy-in was the smallest possible for every component in the system. This still works for a lead-acid battery, and in a power outage where I felt I needed to drag out my solar panel to lay it in the protected back yard...I would first run to the store to buy two 12V deep-cycle batteries, hoping that they were not sold out.
I could round up several car starter batteries to use for a few days, but...they have thin plates to provide the max cold-cranking-amps possible for starting the engine on a cold morning. It would work, but if I needed to deep-cycle them, they would be worthless in a couple weeks. I wondered about buying a couple deep-cycle lead-acids and then running a long-term storage protocol I read about, but I am skeptical (fully charge, drain electrolyte and store the electrolyte, double-rinse the battery plates with distilled water, dry and store the battery. Re-fill with electrolyte when needed to use).
I wanted to try some way to leverage my recently acquired knowledge about lithium 18650's, but...when looking at the charge controllers and inverters, I was torn between 3S and 4S. Each having its benefits and drawbacks. Since then...I have fallen in love with 7S and 24V for a small system.
Nothing wrong with going straight to 48V (I have three 14S ebike battery packs that I can charge at work, to run a 48V inverter to power my TV). That being said...my 24V research has led me to used 24V UPS's (Un-interruptible Power Supplies). My work computer has a 12V UPS with a small SLA in it. During a power outage, in theory...it would continue to power the computer until the battery drained.
UPS's exist in 24V, and when the SLA inside wears out, sometimes the company simply upgrades them to a bigger and better model, rather than swap-in a new SLA (since the UPS companies often charge as much for the service call to replace the two 12V SLA's as it would cost to simply buy a new UPS). This means that....regardless of the reason...there are used 12V and 24V UPS's available at very reasonable prices. The 24V units seem to take 7S lithium very well, so these are ripe for anyone to snag a few and perform a lithium 18650 upgrade on the guts.
An MPPT solar charge controller can take-in a wide range of input voltages from a solar panel array. A 7S 24V system can be fed from panels that output anywhere from 28V-40V.
I wouldn't try to run a refrigerator off of a small system such as the type I am describing here, but...for a laptop, your smart-phone, and a few 18650 flashlights?...I think this could prove to be a smart move. Here's a 24-min youtube of what I mean: