Oil fired aga / Rayburn ideally need to be left on 24/7 unless fitted with a pressure jet burner even then they need to be on most of the time, they are not easily on and off able as they take a good while to warm up and cool down, for this reason putting this with a solar system will offer no appreciatable saving what so ever.
Adding a wood burner into the equation will add to the complexity, and probably require a non off the shelf cylinder increasing the cost further.
How many of you are in the house?
I very much doubt the £20.00 a day figure for the running cost quoted above, my parents have an Aga and have had for years, admittedly it's only doing the hot water but it costs roughly £5.00 a day to run.
This heats the kitchen, provided 24/7 cooking and clothes drying and provided plenty of hot water for 2-3 people.
They also have solar, but that's all a bit random.