During my first days in Stuttgart i fell into a trap buying tram tickets. The zone thing is very tricky and you have to takenote of prices for different zones. Make sure that you either buy a weekly, monthly or group ticket for the are cheaper and less complicated. Else buy one ticket for the complete journey and not for each stop where you change trains like i did.
Unique Suggestions: Ticket controll is always at random, don´t mess around and think your safe!