Sandy, you have talked about the stove, but what do you have in the way of wood ? $600 for heating an entire winter is not much. Natural gas is the cheapest fuel besides wood, unless you have access to free wood and consider the work of chainsawing, splitting and stacking to be part of your lifestyle, as opposed to something worthy of your time. It sounds like you would not burn much wood to get you through the winter. My uncle goes through about 1 cord per winter and he is in VA just inland from Chesapeake bay.
None of these things are bad, but they do impact how your investment in wood burning is amortized (the "business case", as it were). On the other hand, it is possible that the investment in a better stove and chimney may be financially OK with you. In that case a small steel plate stove runs from $380 (CFM 1000 sq ft stove at Menards) to something in the $700 price range for the small Englander. If it were feasible to run an insulated flex liner down your existing chimney, it would add a lot of safety to your setup, since it seems that the internal walls/framing is too close to that masonry chimney for safety. Bear in mind that natural gas appliances can be vented through aluminum pipe, whereas a chimney for a woodstove is stainless steel double wall with 1" of packed insulation between the inner and outer pipe. NG appliances can never create creosote which is why the venting pipe does not have to be designed to withstand a chimney fire. If you were to see a chimney fire, which is when creosote that has been deposited over time in the chimney finally manages to ignite, it is a very scary thing. Roars like a freight train and sends flame and sparks flying high into the air out the chimney cap. The temperatures can become hot enough to melt the sand in concrete and crack the clay liners. Of course, often before it reaches that point, it gets the surrounding combustibles near the chimney hot enough that they reach ignition.
So that in a nutshell is why woodstove flue systems have to be so carefully designed, and why you want a woodstove that is EPA compliant (because it produces no noticeable smoke, and condensed smoke is creosote).
Having a woodstove lends a particular ambiance to a home, especially the new ones with big windows and the spectacular fire caused by the smoke being burnt by the secondary air system. Its even better than a fireplace. In your circumstance, if funds are tight and you don't already have at least a cord of seasoned wood on hand, I think that going the woodburner route is not the best decision. I live in a much more northerly climate and the winters can be 6 months long with below freezing conditions for that duration and I heat my home with a combination of scrounged wood and some that I buy from a local tree service guy. My total wood bill ls generally less than $500/winter and my utilities (NG and electricity) run less that $75 per month in winter. So for me it is a huge saving (some of my co-workers pay $450-600 per MONTH) on NG bills in January and Feb. That savings allows me to spend more on a bigger, nicer and more expensive stove, because I am still on a budget.
Last year I spend $2200 for a Morso 7110 stove, and about another $700 for the chimney materials, which I installed myself. The stove turned out to have too small a firebox to allow it to burn for an acceptable length of time meaning I was tending it just before midnight every night and then again at 6am every morning. Before leaving for work I would stuff it to the gills and get it cranking and by the time I walked in the door at 5:30 pm the temperature would have dropped down close to the furnace thermostat setpoint (60F). But the savings in NG costs amortized the cost of the stove in 1 season. This season, I will be amortizing the cost of the chimney and the new woodsplitter I bought, which shortened the task of splitting from many weeks to only a few days. I bought a bigger stove (Pacific Energy T5), which will leave my schedule less constrained (longer burns) and the Morso is being installed in the basement living room where it will see occasional use, not 24/7. With heating costs up 30-50% compared to last winter and my cost for wood unchanged, I expect to save even more this season than last, so I should break even half way through next winter. From that point it is downhill all the way.