How to evaluate the suitability of an electric tankless water-heater
The numbers you need are flow rates and desired temperatures. For example, Home Depot's guide gives the following flow rates:

Bathroom Faucet: 0.5 – 1.5 gpm

Low Flow Kitchen Faucet: 3.0 – 7.0 gpm

Shower: 1.0 – 2.0 gpm

Dishwasher: 1.0 – 2.5 gpm

Clothes Washer: 1.5 – 3.0 gpm

Tankless heaters are rated for how much heat they provide at a given flow. If your incoming water is 50°F, and you want 120°F, you need a 70°F rise in temperature. Now say you want to both run your dishwasher and take a shower. On the high end, you may be looking at 4.5 gpm. You need to find a way to raise 4.5 gpm 70°F. Going back to Home Depot, they sell a Rheem gas heater that will do 77 degrees at 4.9 gpm.

Alternatively, you could combine a whole-home unit with point-of-use units. This is particularly useful if you want to only heat your shower to 120, but your dishwasher doesn't include a heating element and you'd like to heat that water to 140, or if you want your kitchen faucet to supply hotter water than the bathroom faucet or shower. Also, point-of-use units are useful for providing instant heat.