If it is a family home with 2 bathrooms and other appliances that could be used at the same time, then stored HW would probably be the ideal.
As suggested, thermal stores are not the most efficient given the temps they need to run at with modern condensing boilers That and they are nicknamed 'sludge buckets' for the reason you can see in your pic. Yes, anyone should clean that mag filter as part of the their boiler service work.
Without knowing the cold mains system - dynamic mains pressure and flow - though I would presume that given there was a thermal store then the mains couldn't be all that bad, then it would hard to recommend an unvented. I would suggest a mains survey is performed by your local water transporter and that'll dictate what options are available.
