How much battery you need really depends on your usage pattern. There like everything else with solar is probably not a perfect solution since you can affect change to get most benefit from many scenarios. Such as you mention, use the white goods on sunny days close to peak generation as much as possible.
This is it really.
Batteries are not right for all setups.
Id say if you have a large, south facing roof so can have a lot of panels, and generate a lot of energy, and you are also a say high electicity user, and also dont work from home, then absolutely.
Although the outset cost will be very high, you may end up almost have a nil eletricity bill in the summer, and significantly reduced during the winter, and that can really start adding up the savings and payback time.
On the flip side of that, if your roof isnt ideal, so you cant generate masses in the first place, and you work from home and get savy with using your washing machine etc during peak generation, you are probably not going to benefit, and that is where you really have to start looking at the statistics and try and work out if its worth while.
I mean, solar panels in general, are by any means a perfect solution, they tend to generate a lot of energy in peaks, and often when you are least likely to use it, whilst during those cold dark winters when your usage is up, they generate the least.
One thing I will say is if you are not getting a battery, and you have a hot water tank, we are getting a device installed that diverts excess into the hot water tank, and it was a very cheap extra. Whilst we have oil fired hot water, there is an immersion heater (which we dont often use) but with the excess energy going to that, it should save a bit of oil. Its also a thing unlike a battery that in theory lasts forever, so like the panels, will pay itself back, id say pretty quickly.