If your goal is to save money you'll need to do the calculations based on your exact location and costs. In Australia the main use of small battery-backed solar systems is for off-grid locations but people are increasingly looking at going off-grid as the cost of the grid keeps rising (mostly due to cheap air-conditioners) while the cost of PV systems drops.
If you're trying to reduce your total environmental impact the calculations become much more complex because you need to first decide what counts as "environmental impact" and how you're going to compare different sorts (see this question, for example), then for each option work out what the impact actually is. I'm going to assume you're just using money as your measure since the method is the same but the process is simpler.
To do the calculations you really must know not just how much electricity you use, but how much of that use can be eliminated, reduced, substituted or time-shifted. The value proposition for all of those changes when you're looking at off-grid power because of the cost of generating and storing it. You can get extremely efficient fridges, for example, but they're expensive. But off-grid the reduction in power consumption is often cheaper than generating the extra power using PV and storing it in batteries.
The sort of battery technology used for houses hasn't changed significantly in the last 20 years, it's still lead-acid based. There are a few lithium battery systems just starting to enter the market now, but if you are not happy with lead-acid batteries I would not suggest buying a lithium one until that market matures. It's still very "version one" right now.
The other way to save money and reduce your environmental impact is to reuse materials. If you're in an urban area you may be able to get "ready to recycle" lead-acid traction batteries, for example, that no longer work in their original application but are fine for you (an electric forklift that only runs for half a day is effectively useless, but a 50kWh rated battery that's down to 20kWh actual capacity is excellent value for $500). Similarly, buying second hand panels and supports might save you money and significantly reduce your environmental impact.
Since you're in Australia I suggest you join the Alternative Technology Association and read the relevant issues of their Renew magazine as this the viability of opting off the grid has been discussed recently. They've been talking about off-grid power system in Australia since they were founded (20-odd years IIRC).