Advice on what to replace heating system with.

Emily11223344

Hello
I am new to this forum so please forgive me if I make any mistakes! We are in the process of buying our first house, which is a two bed terrace built in around 1970. The current heating is an open fire, a back boiler, a few very old night storage heaters and an immersion heater. I'm not 100% how all these things work, but have been told that they are very expensive to run and are very inefficient. In the long run, we plan on installing a log burner downstairs where the fire is, ,which we hope will heat all of downstairs ( very small house, downstairs all one long room), but are not sure on what to do with the upstairs heating and water heating ( there is an electric shower). 
There is double glazing which are wooden window frames, and the house is very small so it's fairly warm without heating.
Because of the house's location we are unable to get gas heating, and the garden is very small, so we would prefer not to have an oil tank ( and only have space for a tiny one anyway)
We have been looking at a company called North East heating, which as far as I can tell will replace everything with an electric heating system, but waiting on quotes. 
Does anyone have any ideas on what the best heating system would be?

Thank you for your help.

J_B

A few thoughts till someone more knowledgeable comes along ...

Yes to a decent log burner - do you know exactly what the 'back boiler' does?

All electric heating has the same efficiency so don't be fooled if Mr North West tells you his heaters are filled with magic moon dust (search the forum for Fishler heaters) Maybe replace the 'very old storage heaters' with newer ones which may be more controllable.

Does the hot water tank have any insulation?

Mister_G

OP posted in the wrong place.  They realised this and have now reposted under Energy and already received some useful replies.