Yes, a good sized solar array could easily cover your needs, but you are right to make the most of it you need to store some for use in the hours you are not generating. Pretty much all this week I've generated 30kWh+ a day with solar, but without my battery I wouldn't have used the majority of it, and even now I am exporting as I can't use it all due to how sunny it has been all week. Car is full, battery is full, water is hot, washing all done, etc. But I have 8.2kWh stored for later this evening once the generation falls off and I can use that, and recharge it again if needs be in my off-peak period to use before first light hits the panels in the morning.
Try and break down your real time usage using the IHD with your smart meter if you have one, and look at where you can shift power use, either from day to night, or from night to day in the better/sunnier months. Getting the most from your system is gathering data, and using that data to make your usage as efficient as possible, be prepared to spend some time doing the optimisation.