We installed a wall-mounted aircon unit in our loft when we did it a couple of years ago.
We'll be putting more units in when we put up an extension later this year, for exactly the reasons you suggest.
Each system comprises the in-room unit, some ducting and the external unit, which has a fan and pump on board. The external unit should have quite a lot of clearance around it, and ideally should be mounted in a relatively cool area, as it has the job of pumping away the hot air from the system.
The internal unit can be set to heat, cool or simply blow as a fan.
We bought an over-specified Electriq unit - think it was this one:
https://www.electriq.co.uk/24000-btu-hitachi-powered-easy-fit-inverter-wall-split-air-conditioner-eiq-24wminv/
The gizmo itself was not so much - around GBP600 – but the fitting was complex, as you have to run the ducting through the house to the outside, and fit the external unit.
Also you need to pressurise the refrigerant in the system, which adds a bit of cost, if you use a general contractor, as opposed to a specialised aircon installer.
You may need one unit per room, unless you are prepared to leave internal doors open.
The cost is more about the fitting than the purchase price of the unit - ZM probably has it about right with 500 for the unit and 1000 for the fitting, but that will depend a bit on how complex the job is for the fitting team.
Good luck :)