Best route probably means the most travelled as a Class 1 & about the easiest. Actually the Eastern route, the one requiring a 4 W Drive, is considered the easiest and it is slightly shorter. But using the Halfmoon road and the Mt Elbert trailhead, you can also do Mt Massive( 12' lower than Elbert) from its trailhead some .1-.2 miles further West on the same road. Massive has 5 summits over 14k and there are about 8-9 trails to the main summit. It is lot longer than Elbert as the easiest trail is some 13 1/2 miles round trip.
Probably one of the more popular climbs is to do 3, some call it 4, 14ers in a 7 mile loop, all Class 2. You drive to Kite Lake which is 12,000' ( I believe there is a fee camping area and there is a fee day hiking area too) climb Democrat, go over Cameron (not considered a true separate 14er) to Lincoln and then finish the loop by doing Bross and back down to Kite Lake. The approach is south of Breckenridge and Hoosier Pass with an entry road West of a small town Alma. Anyone driving in that area beware of speed traps in both Alma and Fairplay which is just south of Alma.