Works best in warm climates (winter here ain’t it)
Electric
Cheap to buy. Expensive to run
Instantaneous are possible but could feasibly only work for a single shower
Gas
Cheaper to run
Some have a pilot light
You could use electric ignition but then you’re tied to the electrical system for hot water
Solar hot water
Super expensive to buy and install, super cheap to run
Need a large tank to handle a string of cold days
Likely cuts a hole in your roof
Storage tank
If you use a lot of hot water
Mild steel will corrode. Need maintenance
There is a sacrificial anode that prevents corrosion of the tank. Replace this every 5 years
Check warranty
Stainless steel is better
Instantaneous
Often only gas does this
“We’ve had members advise that their continuous flow water heaters were not turning on because of a combination of low flow showerheads and too high a trigger point for the hot water heater to start up – essentially, the water flow was not sufficient for the water heating to be triggered. Keep this in mind if you’re considering having low-flow shower heads and a continuous flow hot water heater, and confirm the trigger point is set appropriately.”
Apparently many things (involving drinking or sewer systems) need a licensed plumber