This setup sounds similar to our cottage. Which came with a small 120v electric tank heater (not sure size - maybe 20 gallons?). I have been suspicious of it since we got it, it looks pretty old. But if it ever gives out I will replace it with a new one of the same type & size or maybe even a bit smaller - cheap & easy. Not sure how many showers will be taken in a day at your place, but the small size helps keep people from taking too-long ones. Which also helps with our also suspect very shallow well & water supply.
Ours is plugged into a switched outlet. We turn the switch off when leaving & on when arriving. I was there last weekend, first time in almost a month. Hit the switch & had a nice hot shower an hour later. End of season (coming very soon), we just turn it off (all the power to the whole place, actually), and open a ball valve to drain the whole system down through the floor.
If we were in a place with gas, I might consider a gas heater - but this is just too easy for us, and no maintenance of any kind. And cheap to buy & cheap to run. No doubt gas would be cheaper to run, but with how much it is used, I don't think the savings would be a whole lot - it is only used for washing a few dishes, and the occasional shower.
. I’ve always heard the propane is the better price point but I believe the electric heats quicker or higher temps. I can’t fully recall but I’d definitely go tankless and by what you’re describing I’d go with the propane model.
