Off-grid power systems are for those independent people who plan to live within their means and use only what they produce with solar panels, wind generators, hydro-power, or a combination of these.
Off-grid AC Solar Power Systems provide power for normal AC appliances.
Off-grid DC Solar Power Systems provide power for only DC appliances, as in RV's and boats.
Off-grid Wind Systems produce power with wind generators. Running a household on wind power requires that you live in a really windy (Class 5 or 6) area.

On-grid/Grid-connected solar power systems are the very latest technology, and can be likened to having your own solar power station located on your house roof, that silently generates green electricity for your own use, or any excess can be sold to the electricity supplier, via the grid. It is therefore not essential that the solar power system is sized to exactly match what your daily power usage is. If you generate more power than what you use, the balance is sold to the electrity suplier, and you can buy back any extra power that you may need, at any time, to cover any shortfalls. (eg. night time). Typically, this type of solar power system is sized to maximise the efficiency of the inverter size used, or the amount of funds available, or to take maximum advantage of any rebates available. There is no reason why you can't install a small solar power system initially, to help reduce greenhouse gasses and to reduce your power bills, and then add more solar panels later on, as extra funding becomes available.