I decided on another tank heater. I was tempted by a tankless water heater, but decided that getting a tank in fast trumped a fuel efficient heater. I looked at the cost and cost savings of various types, together with installation costs. In short, it would take me 15-20 years to realize any cost savings from a tankless heater. The new heater costs $419 and the installation is about $320. If I went with a tankless, the cost would be more like $600-700, and the installation way more, as pipes would have to be rejoined.
I teetered on this decision. Both directions were compelling. But the low-flow heat of a water heater (we hand-wash dishes a great deal), and the ability to work without electricity (also key) were deciding factors.