Don't know how much you use BaseCamp so....
.gpx is correct
1. On a pc File>List and name the list. Test
2. Next File>Import into Test (Browse to the file your trying to import) highlight the file and open. The file should now be in BaseCamp. The contents of "Test" shows up at the bottom of the column. Double left click your Route or Waypoints in Test and they should show up on your map.
If your using a mac, these directions should work.
To upload to your garmin you will need to tether your garmin to your computer.
and use Transfer (mac) Device (pc) to make the transfer. The route will show up on the Garmin under Apps > Trip Planner. Any waypoints will be in Where to > Saved