Choosing the correct tankless water heater propane system for your 3-bathroom living space just takes an honest view of the actual water usage you will have. The number of bathrooms does not tell the whole story. Where is the location of the home? Colder locations require higher-volume units to produce enough gallons per minute to accommodate a couple of people and a house full of guests. The next question you have to ask is how often will more than one shower or bath be running simultaneously? Will the water heater be installed indoors (which would require proper ventilation) or outdoors?
In my vacation cabin, which is in a cooler climate, I have two bathrooms (one with a shower and one with a tub). We installed the indoor propane-powered Rinnai RL75iP (https://amzn.to/2JJkpFq). When our family goes to the cabin we usually have from 4 to 8 guests (sometimes up to 12) and we always seem to have hot water for all the guests. Since most of our guests take showers, folks are taking showers one after the other or at different times during the day. That said, when I’m running the bathtub and the shower at the same time, there’s enough hot water generated for both. Therefore, I recommend, at a minimum for a 3-bathroom home that sometimes has multiple guests, a whole-house unit that produces 7.5 – 8 GPM of flow in warmer climates especially if the majority of the time there are only 2 persons in the house.
The beautiful thing about tankless is that even if you have 10 people taking back-to-back showers, you will never run out of hot water like you would with the old tank units.
Rinnai and Takagi are two of the best brands for whole house propane units: