Q:

Which projection is best for mapping the contiguous United States? 

If I wanted to project latitude & longitude data for the contiguous United States (the United States excluding Alaska and Hawaii), which projection would I use?  I prefer more accurate distances followed by shapes

A:

The Albers equal area conic is the typical projection for historical USGS maps of the lower 48, it being a general-purpose low-distortion compromise for mid-latitude short and wide extents.  
As a reference on map projections, I like the ESRI book Understanding Map Projections.  Its first 30 pages are not unlike a short textbook, followed by ~70 pages of appendix on individual projections, their uses, strengths, weaknesses, etc. 

Albers, pg 37
Lambert, pg 66
equidistant conic, pg 53 

A:

ESRI has defined three projections especially for the contiguos United states.  These are included in QGIS as well:
EPSG:102003 USA_Contiguous_Albers_Equal_Area_Conic
+proj=aea +lat_1=29.5 +lat_2=45.5 +lat_0=37.5 +lon_0=-96 +x_0=0 +y_0=0 +datum=NAD83 +units=m +no_defs

EPSG:102004 USA_Contiguous_Lambert_Conformal_Conic
+proj=lcc +lat_1=33 +lat_2=45 +lat_0=39 +lon_0=-96 +x_0=0 +y_0=0 +datum=NAD83 +units=m +no_defs

EPSG:102005 USA_Contiguous_Equidistant_Conic
+proj=eqdc +lat_0=39 +lon_0=-96 +lat_1=33 +lat_2=45 +x_0=0 +y_0=0 +datum=NAD83 +units=m +no_defs

So it is up to you which projection characteristics you need: equal area, equal distance or conformal. 
Visit this page to see the differences: http://www.radicalcartography.net/?projectionref

