Assuming not a full ducted system as you would possibly choose for a home re-fit. Something cheaper with external refrigerant runs with interior emitters ideally on external walls, is a good way to go, IMO.
Cooling mode works a treat and it only needs to be a degree or two lower to feel good on a sweltering day. Heating mode can easily be supplemented with a few cheap oil filled rads on timers.
Solar PV and some battery storage are an obvious addition to the plan but can be added at any time as funds permit.
As for DHW, I'm a big believer of simple immersions on night tariffs, mine is currently 2.99p per kW midnight to 0600. At those prices IMO it's not worth chasing COPs from other complex, expensive and disruptive installs which are better used as part of big refurbishments.
I'd use a Solar thermal linked to the cylinder with the immersions, two, or even, three spaced and individually controlled. All relatively cheap and works a treat, and in winter the solar thermal supplements the immersions. Roof fit or even vertically on a suitable wall.

Other thing to consider as part of a wider preamble to the above would be to have a look at the home electrics right the way from the meter to the CU and beyond. Although modern "stuff" is pretty good for efficiency, best to make sure the house electrics are up to it and you have enough CU capacity to cater for extra timer breakers to optimise the night cheap rate use.

My ducted system is great, but it's only in half of the house. When funds permit I'll be adding a 3 split system to the other half and I'm confident enough now to start ripping out the old wet system radiators where not needed.