Galvanized potable plumbing, yes, replace it- better to do it all at once than a section a time. If heating system plumbing it may be OK- you'd have to crack it open and see. In a closed pressurized loop you don't get much internal corrosion on the pipe, but with oxygenated fresh water you sure do. There's a lot of 50+ year old iron heating system plumbing still in good shape, but there's also some that's pretty much toast.
Cast iron, or fin-tube baseboard? How many feet total?
With a "K-factor" stamped on the oil bill we could take a pretty good WAG as to what the design condition heat load is, even if you were only keeping it 60F in there (or even lower.) But if it the house is insulated (or will be), has double-panes (or reasonably tight single-panes + storm windows), and doesn't have a sea of recessed lights penetrating into the attic for maximal stack effect, it's very likely that your heat load will be under 50KBTU/hr, and may be under 30KBTU/hr. With enough baseboard you could heat the place (and get hot water) with a condensing hot-water heater (with an isolating heat exchanger for the heating loops) at low temp/high efficiency.
Since it isn't air-conditioned, if it has a reasonably open floor plan you could also probably heat it most of the time at lower cost with a inverter-drive 1.5- 2-ton ductless mini-split heat pump for a lot less money (less than half) than heating it with condensing propane, which would also serve as highest-efficiency air-conditioning. (A 2-3 head multi-split can work if you really need extra zones/rooms.)
It takes a bit of self-training, but the Taco heat load calculator is a professional type tool for doing room-by-room and whole house heat loss calcs on, and costs you nothing more than your personal vectors. Be sure to dial the ventilation rate down so something reasonably retrofittably tight (0.25-0.35 ACH) and adjust the outside design temps to something no lower than the ACCA 99% values which will probably be around +5F, rather than using the tool's defaults, which are sometimes more than 5F lower.
And assume it's the post-fixed up condition, not the current condition. If timber-framed, it's worth retrofitting blown cellulose into the cavities right over the existing R8-R11 batts, which fills in all voids and lowers the infiltration & convection losses significantly. Air-sealing the ceiling then taking it up to at least current code-min with blown cellulose in the attic is also a good value. If single-paned but in decent shape, tight low-E storms over the old windows is cheaper and higher-performance than middle-of-the-road double panes. The basement walls may wait if you're not planning to convert it to living space, but it's likely to be a double-digit percentage of your total heat loss. The rim joist and foundation sill SHOULDN'T wait, since that's typically the single largest un-treated air leak in a house, and located for maximal stack-effect. Closed cell spray foam at 1-2" thickness would both insulate and air seal, but you can also do it with cut'n'cobbled rigid foam board, sealing all edges and seams with 1-part gun foam.
If you ARE going to insulate and finish the basement, search out those topics on the remodel forum of this site. (Ducts would probably cut into headroom down there, if that's at all in the long term plan- another reason to stay ductless.)
If it's not already, odds are good you can get the whole house heat load under 25KBTU/hr @ +5F without breaking the bank, and with even 75' of baseboard you could run a boiler or condensing water heater at 90%+ efficiency 100% of the time. At current propane prices it's pretty easy to rationalize a condensing burner, but you might still consider supplementing it with a mini-split. At +5F the coefficient of performance (COP) of a better mini-split will be about 2.0, and comparable to heating with condensing propane, maybe only slightly cheaper (it depends on your utility rates and propane pricing) but at 25F it'll be running a COP of 3+ and quite a bit cheaper. And at 45F you're looking at a COP of 4, less than half the operating cost. Ducted systems don't do nearly as well, even with near-perfect manual-D designed insulated & sealed duct systems the air-handler power takes at least a whole number off the whole-system COP. In a central OH location a good mini-split can challenge even geothermal heat pumps on heating season performance, at a fraction of the cost. (Figure ~$4-4.5K for a 1.5 ton, ~$5-5.5K for a 2-ton, installed.)