We had the same thought a few years back in our first home, and we ended up ripping out the existing zero-clearance fireplace (and the wall all the way up to the ceiling) and refinishing the newly created alcove with a woodstove that fed into the existing chimney. (Think of a space big enough for a recessed tv or large fish tank, but with a woodstove in it.) Our house layout and size and zoning allowances (and a DIY-inclined inspector) made it the most logical choice. In total, it cost around $750 for the stove, the chimney piping we had to replace, the fireproof wall material (you can't just use normal drywall) and the odds and ends of material to make everything legit. It worked beautifully to heat our entire living area, kitchen, and all the bedrooms on that floor. And we were able to do the work ourselves, as long as we brought the inspector in at the appropriate stages to approve the work.
Fireplace inserts can indeed be pricey, but there's a huge range available, with a corresponding range of prices. A note: inserts and woodstoves are not the same; an insert fits into the wall, whereas woodstoves are freestanding appliances. Woodstoves are generally cheaper and are less complicated to install. (They may also raise your home insurance cost.) If you would prefer to use the existing opening, you first need to figure out if it's even feasible - if your existing fireplace opening is too small for the smallest insert available that'll do what you want it to do, it becomes a good deal more expensive to do a renovation.
When you say supplement your heating with fire, do you mean having a nice fire going on weekend evenings, or are you going to actually try and heat your home? We do the latter and burn through around 10-11 face cords a winter...which means we start around now and it's pretty steady until late April, early May. A face cord of hardwood around here (Ottawa Valley) can run anywhere from $100 to $150 delivered and already split. In order to avoid that expense, we collect it for free from people who have cut down trees, windstorms, etc, from spring right through fall, bearing in mind that we have to let it season as well, so we're actually working a year ahead. And it costs more in house insurance, because a woodstove is considered a fire hazard.
In regards to the furnace, you'll want to check with your local zoning codes to find out if it's permitted to have a wood-burning furnace - not every municipality will allow them, depending on how pollution-conscious they are. Also check the physical requirements for clearance of a wood-burning furnace; if you have to expand your furnace room to accommodate it, you won't be saving much.... ;). Bear in mind that you'll need a vent/chimney/etc for it, so if your furnace room isn't currently on an outside wall, you'll have to consider the logistics of how you'll need to modify your ductwork once you move the furnace (or build a chimney right up the center of the house). Just a few things to consider....
We've looked into a wood-burning furnace ourselves, and have had to veto it just based on the up-front cost. The best efficiency rating we were able to find was 86%, and that was totally dependent on what you were burning....oil and gas furnaces are a good deal more efficient, from what we've found. Wood just isn't that efficient compared to the available alternatives....but it's such a nice heat; feels way better than our forced-air furnace. :)
If you're just looking to have the occasional fire in a fireplace in order to turn the thermostat down a couple of degrees, personally, I'd go with upgrading your existing fireplace into either an insert or a woodstove.
