Eurocity Innsbruck - Verona     : required (for the Italian leg) - you will have to pay an extra fee. More information can be found here and here.  
Intercites in France   -              :  required   
Eurocity Frankfurt - Milan        :  required (for the Italian leg)
ICE Hamburg - Zurich             :  optional (OBB nightjet - required)

This information including prices can be found here. 

If you would like to avoid reservations you can go to planner in the Rail Planner App and tick the box '’avoid reservations'’.

@seewulf, as you are really an expert on reservations, do share additional information, tips & tricks if you have any. 

Cheers, 

To avoid the fees on some routes:

take the EC only until Brennero. From there Regional trains.

Same for Frankfurt Milano. Take the train to Brig or Chiasso/Lugano and continue by regional trains.