I had a rayburn in the kitchen for hot water so didn't connect the woodburner into the hot water system, although I have no doubt it could have been done. Had solar panels on the roof for hot water in the summer and an immersion heater in the hot water tank for when the solar heating didn't work.
As for wood use, it depends on who is filling it up. Was much more economical if I was putting the logs in, rather than ex wife or the kids. Mine is a multi fuel one so can use coal if I want to.