(Edited to provide additional info)
My wife is looking to buy an old house (I'm guessing 19th century) that'll need a lot of renovating, including the heating system. Renovation works will include (some) insulation and modernisation of the electric system. Actually the part in which we'll be living seems to have been a farm building; what appear to be the old living quarters are in a small attached house that hasn't seen occupation for at least 40y, from the looks of it. Both are built with local limestone (probably raw-hewn "stones" behind a layer of plaster), meaning there's only so much wall insulation you can install without losing precious internal space. But the obligatory energy-loss assessment is surprisingly good, despite the fact there are no double-glass windows except in the attic (thanks, Velux!).
Currently there is a central heating system that runs on fuel oil which also provides the hot water (except in the kitchen), backed up by a fireplace insert (one of those sealed things) in one of the rooms, plus an electric radiator here and there. We're currently in a rented house which also has individual electric heaters. We are used to in-house temperatures that peak at 20°C at most, 18°C being the more usual average; we wouldn't even want it hotter and having to put on 2 extra layers of clothing plus coat before going outside.
Most likely we will be wanting to get rid of the fuel boiler, either ASAP after getting the house or in the year or so following the acquisition. A single fuel delivery is around 1000€ which corresponds to about the number of individual electric heaters we'd need. It would also cover much of the price of an electric replacement for the fuel boiler, depending on whether we'd opt for a model that also provides hot sanitary water (we'd want a hot water boiler anyway).
I've been reading up on the topic and while electric boilers are clearly the least expensive to buy and install (and maintain) they're apparently the most expensive in use, compared to other energy sources for central heating.
I have not found a single text that compares them to a system with individual space heaters. Can anyone here help with that question? In particular, will a central heater burn more energy if you do not heat all rooms all the time (shut off radiators, manually or via a local thermostat)? Will individual heaters heat the room more efficiently for instance because they get hotter (e.g. oil-based ones that are safer and give less dry heat)?
Our budget doesn't really allow for other alternatives that are more economic in use (or greener), like those using wood pellets or a heat pump. I know running costs of such systems will be lower in the long run but you have to be able to finance the initial investment.