In Step 1, (see image) BaseCamp will arrange the way points in alphabetical order.
In Step 3, BaseCamp keeps them alphabetical when you create your route.
Right click on your newly create Route and select OPEN.

In the next image, look at the Green Cross.
Above and below the Green Cross are
up and down arrow icons.
Select a waypoint, then click the up/down arrow to change the waypoint order.
Note the small "clock" icon below the Green Cross and arrows. That will set departure/arrival times.
After you move your waypoints to your desired order, click the "Recalculate" button at the bottom of the screen.
The Green Cross is so that you can add more waypoints.

I've probably forgotten something, but keep chipping away at it.
And remember that Google Maps can be useful when it's available.