For budget ours is also about 3.7, but it's also a large double door burner which is half of the total cost, in addition we also need scaffolding ( -access tower) due to the height of our chimney.
I think average price is about 1500 for all the installation, liner etc and then whatever the wood burner costs on top of it. You can also buy them second hand off of places like eBay.
You can get woodburners installed if you have no chimney or,fireplace, they look great and simply sit someplace in the room, I think they go up through the roof, not sure, and also you can get them inset, which means they are inset into the fireplace, a bit like a tv hanging on the wall but it's suspended into the fireplace, but is actually a full size woodburner.
The size uou need depends on the size of the room, and also the size of your fireplace, and I understand the cost of wood is fifty percent of that of electricity, so it pays for itself at some point.
Apparently an open fire is 20 percent efficient, so 80 percent of the heat goes up the chimney, and a log burner is 80 percent efficient, so only 20 percent up the chimney, so more cost effective to run and heats the room quicker.
Anyways, this weekend I think we will go shopping for the stuff for it, I fancy one of those really big log baskets. I did see one on Amazon which was just two glass side panels joined together by two steel bars, and made your logs look like they were suspended in the air, but think it's too modern for our place. It was also nearly two hundred quid!