Fixing a bathroom vent exhaust going only into attic
The vent should not be placed directly under the eave.  The external cover of the vent when mounted on the wall protects the vent from rain.
Standard galvanized duct piping is used.  Yes, it is the same as the vent duct used for dryer.  You would just use the same ducting type that is vested to the attic.  
Exact placement on the exterior wall is also depend on where you route the duct in your attic. 
1. Will it block storage space
2. How will you suspend it
3. On the rafters.
This is a picture of vents on the exterior wall.  The vent ducts are round, the cover is a rectangle cap