What size of house? To get under £100K is doing well, I doubt I will achieve that in spite of me doing so much of the work myself.
As Peter says, No 1 is insulate, insulate, insulate. No 2 is air tightness. No 3 is good doors and windows, No 4 is an MVHR unit (mechanical ventilation with heat recovery)
Then you can think about heating, which should not be much. I am going for an air source heat pump and to buy one for self install should be under £1500, possibly under £1000, i.e not a great deal more than an ordinary boiler.
I personally would not have oil or LPG again, the price is too volatile. (though I will have LPG for cooking, the usage is so low that the cost hardly matters)
I will be fitting solar PV, but by the time I get there, I doubt the (already low) feed in tariff will exist any more. So that means a DIY installed system bought as cheap as possible, and almost certainly some form of battery storage to ensure near 100% self usage.
Tell us more about your house design and where you are building.
Oh and welcome to the forum.