There are some free applications that let you try and play with projections.
They also indicate to what extend they preserve size, shape or direction. Depending on you application a different priority might be set. For instance if I had to map an areal phenomenon like e.g. certain species habitat zones I'd prefer a projection that preserves size. There are projections that make a good compromise of all three aspects.
For mapping the whole US or North America in general Albers Equal Area Conic or Lamberts Conformal Conic are a good choice for most applications.
Indiemapper says about these projections:
Albers Equal Area Conic (Heinrich Albers, 1805): Like Lambert
Conformal Conic, this is a very popular map projection for the US,
Canada and other continental/large countries with a primarily E-W
extent. Used by the USGS for maps showing the conterminous United
States (48 states) or large areas of the United States. Used for many
thematic maps, especially choropleth and dot density maps.
All areas on the map are proportional to the same areas on the Earth.
Directions are reasonably accurate in limited regions. Distances are
true on both standard parallels. If you are making a map of
conterminous States, use the standard parallels of 29.5N and 45.5N.
Scale true only along standard parallels.
Map is not conformal, perspective, or equidistant.