With a household of 4 you'd want the biggest heat-pump water heater available. If your water volume use is high it would lower the temperature of the basement considerably, but it would also provide substantial dehumidification.
I'm not sure if the GeoSpring still has all the issues that they were stumbling on a few years ago, now that production has moved from China to Kentucky, but I believe that was WHY they made the change.
All heat pump water heaters are a bit noisy, so putting one directly under a bedroom may not be ideal.
Whether the water heater is the most cost effective way to reduce oil consumption isn't clear. It might be, but usually not. It just depends.
With an oil boiler in the basement, the basement is being "conditioned", whether you're intentionally heating it or not. Air-sealing & insulating the band joist & foundation sill and all known window/door/plumbing/vent/chimney penetrations into the basement is often the most cost-effective $500-1000 you can throw at an old house, since it blocks the bottom part of the stack in the "stack effect", dramatically reducing the amount of stack-driven infiltration that's going on 24/365. Air sealing between the top floor ceiling and attic floor is also a big winner, and usually cheaper than the band-joist. Sealing both the top & bottom of the house is HUGE for reducing the heat load, and always cost effective. To seal around flues requires sheet metal and fire-rated mastic or foam, but flues chases are often direct leaks from the basement to the attic, throwing away heat in winter, and sucking in humidity during the summer. Electric & plumbing penetrations into the attic can usually be sealed with can-foam.
Insulating the foundation walls (at least down to a couple feet below grade) is more expensive, but also has rapid payback when heating oil is the fuel.
Air sealing the top & bottom of the house and insulating the foundation could easily reduce oil consumption by 25%. So if you're burning 800 gallons of $4 oil per year, that investment is paying back about (200 gallons x $4=) $800/year after-taxes. Installing a heat pump water heater would replace your (100 gallons? 150?) of oil use, but add about 1/2 the cost back as extra power use. (Depends a bit on your power rates, how much dehumdification is being offset, etc.)
If the first floor has a reasonably open floor plan and the house can accommodate it, installing a ductless mini-split heat pump (even a 3/4 tonner) can displace enough oil with electricity at operating cost low enough to pay for itself in oil savings in under 3 years. (Some people are getting rid of their oversized oil-burners entirely going with ductless heat pumps, but that's not always the best solution for an old farmhouse.) The hardware is pretty cheap, and most of the install can be done as DIY if you're handy, though it's generally better to let a pro do the final purge/charge/test commissioning unless you already have the necessary refrigeration-tech tools & experience. A mini-split also provides very efficient and very quiet air conditioning without eating up window space. A pretty good 3/4 ton unit is comparable in hardware cost to a heat pump water heater, and would probably have a faster payback than a heat pump water heater. A 1.25 tonner isn't a whole lot more expensive, and if properly sized for the space could cut your oil bill by half or more (depends on the house, the layout, the R-values/U-factors, etc.)
I don't know whether any of this works for you or what breaks the budget, but kick it around a bit before pulling the trigger on a heat pump water heater. In general, fixing the heat leaks on the house provides more comfort than adding a mini-split but after the low hanging fruit on the house is mostly plucked there's very good bang/buck in displacing oil heat with ductless heat pumps in your climate. Whenever I read "oil boiler" in conjunction with "unconditioned basement", I'm inclined to attack the issues with the house first, the space heating next, and water heating would be a distant third, even when dealing with a tankless coil in an oversized oil boiler.