Although tankless water heaters have been around for 60 years in some parts of the world, they are still "untraditional" in the U.S., and I strongly recommend consulting with a plumber who specializes in tankless systems. A specialist typically will have received factory training and will be familiar with the capacities and other requirements.
As with so many technologies that can be considered green, there are trade-offs to balance. These depend on the specifics of the job at hand and the context you are working in. Generally, advantages to the tankless system are energy savings, space savings, and "endless" hot water. Disadvantages include first costs, which are typically greater than for a tank-based system. There is also the possibility of increased "warm-up" water use (or the complication of installing supplemental booster units) if fixture layouts are not close to each other and to the heater unit. Also, some homeowners consider the water-heater tank their backup water supply in case of natural disaster.
Before settling on a tankless system, I recommend that you review your home layout with a plumber who installs both traditional and tankless systems (and is interested in avoiding callbacks). The tankless systems work best when there are short distances between the heater and fixtures, and the fixtures are clustered. A "cold water sandwich" (a pocket of water in the pipes that has cooled in the time lapsed between the last fixture demand and the faucet you just opened) is more likely to occur if distances between fixtures and heater are great. Likewise, supply line layout will influence performance, so you should review the existing layout with your plumber. Size unit(s) accordingly; extended layouts may call for multiple units.
Special features to consider include thermostatic controls that allow a heater's output temperature to vary relative to the inlet water temperature and flow rate, which could accommodate a booster function for a future solar-thermal hot water system. Another helpful feature is an electric ignition device that avoids energy loss from a standing pilot.
To prevent backdrafting of exhaust, installers should address the heating unit's proximity to operable windows and other openings, per manufacturer recommendations. Carbon monoxide monitors should be used throughout the house as a precaution. Review requirements if an installer suggests sharing flues with another piece of equipment like the furnace; dedicated flues will be required in most cases. Confirm routing and separation requirements before committing to a specific model.