I have posted about Aga's/Rayburns somewhere on here before. So here goes....
Aga's in my opinion are not an option (sorry to you 'round lidded people'!). Fine in a big hoose, with plenty of money. They are nothing but a huge, expensive cooker. If you have lots of room, you can have one with an additional boiler which can do the heating/hot water, otherwise you need a conventional boiler for that.
Rayburn's however are a different kettle of fish. (Hooray I hear from all the 'square lidded people'!). Rayburns do both cooking, hot water, and, if it's reasonably new, heating too. I grew up with a solid fuel one which only did cooking/hot water, but it heated the big kitchen (where we all lived), my parents room directly above, and to a much lesser degree, my room directly above my parents one. Not sufficient mind to deal with the premafrost on my bedroom window. This was, pre central heating in the 70's mind!
We bought a new oil Rayburn when we renovated the house 3 years ago. I would not be without it..... I regularly look at houses for sale on the interweb, and it's almost the first thing I look for - a Rayburn. No Rayburn, and I stop looking. Not that we are looking to move mind!
Older Rayburns are not well insulated (and therefore heat the kitchen too much in the summer) and not particularly efficient (unless it's a solid fuel one). Unless you buy new, or one that's only a few years old, heating will be limited to a couple of rads. A new one will cope with a whole house though.
Gas and oil ones (ours is oil) are very very controllable. There are 3 seven day timers. One for the cooker, one for the hot water and one for the heating. They all come on and off at the times you set. Our heat is also driven off a digital room thermometer - if the temp drops below a 14C the heating comes on (at any time - so there will be no burst pipes if we are away) and to the set temp in the evenings when we are in. The Rayburn fires its self up when extra hot water is needed to the rads.
We have a full tank of hot water all day and the water burner is only on for about 20 minutes just before 5pm. All at mains pressure too!
Cooking is fantastic - I don't understand why people seem to worry about cooking in them (friends recently fitted a second hand one, and at their recently party, whilst I was warming my derrière on the Rayburn, the roast pork was produced from the electric oven.......

)
We now cook everything from scratch - including bread. The ovens are vented up through the chimney, so boiling tatties, or pasta is done inside the oven. Bring the tatties etc to the boil and stick the pan in the oven - no smells, no steam. Soup is done the same way. The floor of the oven can be used as an extra hotplate if you are cooking for lots of people and the roof of the oven is the same as a grill. The lower oven can be used for slow cooking casseroles etc or warming plates (or drying your Yorkshire Terrrier after it's bath, as was done when I was a wee boy hehe). A full Sunday breakfast can be done in the big grill tray in the oven. The only bit that's cooked on the top hot plate is the toast! Mine is done on there every morning. Porridge can be put in the lower oven when you go to bed at night and it's done to perfection when you get up in the morning.
Sheets folded and laid on the top of the hot plate lids both dry
and iron themselves overnight. Wet boots dry, socks warm, herbs dry, butter softens for baking, bread dough rises........ I could go on!
Ours being new is 88% efficient. Older ones, like older boilers will be less efficient. We get all our cooking, hot water and central heating for £600 a year at current oil prices. When we fitted the Rayburn in 2004, oil was half the cost, so £300 was excellent! A new solid fuel one, if you have time to chop logs etc will eat anything...coal, coke, anthracite, logs, rubbish, tattie peelings, former Labour Prime Ministers, tax inspectors, etc etc.....
They are expensive mind, this one was £5000. But it was the best £5000 we have spent and we would not be without it.
Reconditioned ones:
http://www.lintongreen.fsnet.co.uk/
Aga Rayburn (they are both made by the same people):
http://www.aga-rayburn.co.uk/