What are common routes from Shadowdale to Waterdeep?

The party I DM has completed their adventures in the Dalelands (Shadowdale and Daggerdale) and wants to travel to Waterdeep. The party is fairly low level, so their travel will be non-magical and not too expensive. The time period is the 1350s DR, the geography is similar to 5e but not to 4e. What are common routes from Shadowdale to Waterdeep? Bonus points for the time various routes take.