"If you are adding living space it is always a good idea to have a
roof" That's the kind of advice I read in those designer magazines.
Next thing you know someone is going to suggest a cement
foundation.

Now, that may not be the most innovative advice you have ever
received but you must admit roofs will tend to keep you dry & warm.

All kidding aside, the selection of the roof ion your addition is an
important consideration, because it will add or detract from the value
of your house.

Most homeowners will choose a shed or gable type roof. If your
house has a hip type roof (Three sided) then I urge you to put a hip
roof on any addition. It cost more now, but your house will be more
valuable when selling time comes around in the years ahead.
 
No matter which type roof you choose make sure you add a roof
overhang with gutters & downspouts. These two items add color &
added design to the appearance.

If you want to go all out then consider a Gambrel or Mansard roof. A
Gambrel roof is a barn roof shape with windows covered by mini
roofs. See one here.
A Mansard is the same except the windows are indented into the
roof instead of being extended from the roof.