When it comes to choosing a tankless hot water system you can have it in any number of sizes and colors. It can run from various fuels. There are lots of quality manufacturers in the market. In fact the choice can be daunting...
The easiest place to start for many is fuel. The tankless gas water heater has perhaps the longest history offering on demand water - the technology is tried and tested and in use in many millions of homes worldwide. Some are using piped natural gas (especially convenient and cheap) and others are using liquid propane. But gas is not going to be for everyone - maybe they do not have natural gas supplies in the area and do not want the trouble of gas tanks or canisters.
There are oil fueled on demand hot water heaters and even combination boilers (that take care of heating and hot water needs for a home). These combis are quite common in the world of gas, but fairly new in oil heating, so shop with care.
There are even high tech electric tankless water heaters on the market. This is for many the ultimate in convenience - almost all homes have electricity fed to their home, and there is no need to introduce other fuels to your home. They heat efficiently, but given the relatively high price of electricity compared to gas and heating oil, they are likely to cost more to run.