Where in Germany are you going? Why not fly directly there?
Where are you flying from?
Zürich has flights worldwide. Basel has flights to Europe, Middle East and North Africa and one seasonal flight to Montréal.
The literal answer is Basel, when you walk out of arrivals at Basel airport you can see the Black Forest.
The sensible answer is choose your airport based on your actual destinations, and what flights you can get from wherever you are flying from.
taking my 14 year old daughter to Switzerland and Germany in April.
1) Which April (2019 or 2020)?
2) First decide where you want to go in Switzerland and Germany, how to travel between them then plan your flights to get to your start and end points. It may well be fly into Switzerland (Basel, Zürich or Geneva, or possibly even Milan if you want to start in southern Switzerland), train to A, visit A, B in Switzerland, then D, E, F in Germany, then train to airport G to fly home.