I had a tankless water heater for years and I loved it. You can get gas or electric, about the size of a box of cheerios. 4 gallons per minute capacity and you could wash clothes and shower and still have hot water. I'm not talking about those little on demand things that fit up under your sink like a Rheem which btw has horrible ratings. I bought a Stiebel which had a ten year warranty. Easy Peasy, also has a thermostat to adjust your temperature.

I dunno about a two/three bathroom house, might need bigger than 4 gpm