The correct solar solution to meet your unique requirements and budget may not even include solar panels or a battery.
The two systems identified above are the two extremes, and both have very different applications.
The UPS (1) offers backup power and energy and is the correct solution if your only requirement is to keep the lights on during periods when the grid utility supply is not available.
The pure grid tied system above (2) will save you money on energy costs but it does not offer any backup power in the event of the grid utility supply being unavailable.
A hybrid solution is a combination of these two systems, and it will offer both backup power and energy while also introducing some savings per month.
A bigger the battery will provide energy for more items for a longer period, while more solar panels will introduce more savings every month.