You can RENT water heaters? Never heard of that.
Regular storage water heaters (both gas and electric) are really pretty dependable, usually lasting 10 or more years before they leak, and maybe needing an electric element replaced or possibly a thermocouple (I don't even think they use those anymore).
What Tiny said about tankless water heaters. Some being far from "instantaneous" and a lot of them put out lukewarm water if you turn the flow up too high.
Myself, I installed a modulating condensing boiler with a water heater tank that is on a loop off the boiler. I have all the hot water I'll ever need, and it cut my gas usage significantly. It would even keep up with my oldest daughters showers if she still lived with us.
[on edit] Don't even THINK of using an electric instantaneous water heater, unless you want to upgrade the electric service to your house. The only thing those are good for are a single lavatory (if that's all you have that needs hot water). Even those pull 3000 watts just to get 2 gpm of not very hot water.