I would recommend:
Buying a Cen-tech laser thermometer. Harbor Freight has them for under $40. You point it at any surface, and it will tell you instantly the temperature of that surface. This will allow you to determine the heat loss on a non-insulated wall vs. an insulated. You can also use it to determine hot and cold spots in the heating system. It will tell you the temperature of the air coming from a forced air vent, too. You can measure from the inside and outside the house as necessary.
Here are the things I would consider (some of this is repeated from above - all good suggestions).
I'm sure you have thought through this, but make sure you are not in an historical preservation district. If you are, you will not be able to do vinyl windows or other "modern" appointments to the outside of the house.
Assuming you are not in such district, and are not trying to maintain an historical Victorian look, go with double-pane vinyl windows. There is a company in Indiana that will do a standard double-hung for $190 installed. They will come measure for free and then give you a quote. I'm sure there are such contractors in your area. They are nice quality - not cheapo and not high end, but they definitely help with energy. They easily pop out for cleaning. I bet the greatest heat loss is through the windows, not the walls, but you won't know until you test. Also, I would not waste money on storm windows. They are not airtight and typically have low R-value benefit. Avoid the "replacement window" companies that commonly advertise on the radio. They will charge double or triple for the same window.
Add spray foam insulation in between the studs in the lower level. As Michaela mentioned above, you punch a hole in the wall (or sill/base plate, if accessible) and fill the voids with foam. You can DIY this or have a contractor do it. If you have a contractor do it, get three quotes.
I agree insulation for the lower floor. Make sure you observe building and fire code. Some jurisdictions will require you to drywall over the insulation because insulation cannot be left exposed in the ceiling of the basement. This is especially important if there are any mechanicals or appliances in the basement. You may be able to avoid drywalling by using fire-retardant spray foam insulation instead of fiberglass batting. Again, check code to make sure.
If you decide to replace the heater, look at multiple options for your location. E.G. forced air, radiant floor, and split unit heat pump. Make sure your HVAC contractors explain the math used to determine the heater size and type. Sometimes, contractors will come in with a quote for an inappropriately sized unit because that's what they have on the shelf at their shop. I would get three different quotes/ideas to make sure you are getting the proper BTU, price, and CFM (if applicable) on the heater.
J Scott's book on estimating rehab costs is a great reference guide for all of the above. It's available on BiggerPockets as a PDF download.
Good luck!