If the oil-fired furnace is from the '70s, methinks it's service-life is pretty much had it (although I've seen folks patch, prod, & limp 40+ year old oil furnaces along forever- to their financial detriment.)
It kinda depends on how much cash you have to invest, but if the ducts are in good condition and reasonably well balanced from a flow point of view (no overheated or too cold rooms) putting in a properly-sized condensing furnace just isn't all that expensive and you'll likely use half the source-BTUs a season as an aged oversized oil-fired beast. Most early '70s furnaces were in the ~70-75% combustion efficiency range when new, and after 35 years of benign-neglect are running ~60-65%. Then, if it's 200%+ oversized for the heat load, as is typical (especially if there has been any insulation upgrades), the as-used AFUE is then only 75% of it's raw combustion-efficiency, or around 45-50% of the BTUs in the oil showing up as warm air in your living space.
eg: If you used ~1500 gallons of oil last year, that's ~2000 therms, and you'd use around ~1000 therms of NG with a 90%+ AFUE condensing system. If you just went with a retrofit gas burner on your antique furnace, with the burner sized properly for the load and tuned to ~80% combustion efficiency (no higher, or you'll condense in the unlined chimney) you'd likely use around 1500 therms (more, if oversized.)
Do a Manual-J type heat loss calculation no matter what. If your heat load is under 100KBTU/hr on the coldest hours of the year (probably is, unless the house is huge or located at the artic circle), for more money you can go with a combined furnace/hot water heater, or use a tankless HW heater/tiny condensing boiler with a "hydroair" hydronic coil in an air handler (preferably with a super-efficiency ECM blower, since your old one probably uses 500-1000watts instead of 100-300W) to heat both the house and hot water with minimal standby losses, and a higher overall annual net-efficiency.
Higher than ~83% efficiency systems won't be able to use the chimney, but 90%+ efficient burners can be side vented using cheap PVC vent pipes (cheaper than a stainless chimney liner by quite a bit!). The installed cost of a mid-efficiency system may be higher than a high-efficiency version in your situation.
On any hot air delivery system, sealing all duct seams & joints with duct-mastic improves efficiency and lowers the noise. Tape doesn't quite cut it in most apps, but if your ducts are still shiny-clean, 2" aluminum FSK tape can work almost as well as mastic.
See if you can't get some competing quotes (with a written heat-loss analysis, not a "35BTUs per square foot" or similar wild-assed-guesstimate method) for a condensing gas furnace at least. Quotes on combi-systems are more complicated, unless you luck out and find the right contractors, but most can handle condensing boiler + indirect hot-water + hydro-air coil systems, which will be more expensive, but more flexible if you think you'll ever want to retrofit something cushy-cozy like, say, radiant floors or low-temp hydronic panel radiators etc. You may be pleasantly surprised how good the ROI on a higher-efficiency system is.
If your duct design is all unbalanced & drafty with leaky rusting ducts, you may want to opt for a zoned hydronic system to even things out. Designing for low temp (under 130F water) on the radiation (baseboard, radiant floor, or radiators) you can meet/beat condensing furnace efficiency and achieve a higher comfort level. (This is LOTS mo' money, in many cases, but if you have the wall-length for going with low-temp cheap fin-tube baseboard it's not as bad as you might think. It can sometimes be done for under $10K in smaller houses with simple layouts.)
Hot air delivery systems are inherently less efficient than hydronic (pumped hot water)- they rely on air pressure differences to achieve the air flow, and this drives air-infiltration in/out of the walls of the house displacing heated air with outdoor air. And ducts have orders of magnitude higher surface area than pipes, losing more heat to basements/crawlspaces/attics when run in un-conditioned spaces. This typically adds up to 10-20% higher fuel use than with equivalent-efficiency furnaces/boilers, depending on the air-tightness of the house. Air handlers also use an order of magnitude more electricity than pumps. If you're on the edge of biting the bullet for a whole new system go hydronic.
Too much to think about? :-)