if (most likely) the outlet emerges horizontally from the back, and goes into a socket through the wall, or into a sloping soil pipe that goes sodways tpwards a duct, measure the height of the centre of the outlet from the pan.
If (less common) the outlet emerges vertically and goes into a socket in the floor, measure the distance from the wall to the centre of the outlet.
If the bathroom is cramped, and you want a WC that does not project far from the wall, you can get a Short Projection WC.
I expect you have a "close coupled" WC where the cistern is attached to a shelf that comes out of the top rear of the pan, at about seat height. These are most common and easiest to find. If you have a separate cistern attached to the wall above the pan, with a pipe linking them, and want to retain the old world look, they are still available.
Modern WCs have a low water content flush, and it is common for people to complain that the flush is inadequate. I suggest avoiding unbranded imported WCs from DIY sheds or budget suppliers, and getting one by an established British maker. I am very happy with Twyfords. If you want an old fashioned style, Armitage still make old designs popular with vintage hotels and country houses, at higher cost.
You should be able to find a technical drawing with dimensions shown. Check that the soil pipe outlet matches your existing for an easy fit. The water supply pipe to the cistern often eters from underneath, sometimes from the side. A plumber can alter the pipe is necessary.
edit
I see Twyfords products are being rebranded Geberit - see here
QS sometimes have good prices.
if you really want a back-to-the-wall or concealed cistern, tiled over, feel free, as long as you don't mind me pouring scorn on you when it goes wrong and repair is a major job.
Don't buy a square bog unless you've got a square arse. A new seat to match will cost a fortune, or be unavailable.