My ideal setup
A (convertible) Tablet PC that can be used with a pen. You can then use OneNote to take handwritten notes while at the same time recording audio from the lecture. The nice thing about this approach is that your notes will be linked to the audio, making it easy to go back in time mentally. Whenever I've used this type of approach, it always amazed me how hearing the 'sound of the room' enhanced my ability to get back into the flow of the material/moment.
As long as your tablet is running a 'regular' (non-ARM) processor you can also then run Mathematica on you machine at the same time, switching back and forth between your notebook taking app of choice (Evernote is an alternative to OneNote). FYI, when taking class notes, I almost always used my tablet in 'laptop mode' so I could type or use the pen as needed.
If you only have a laptop, I'd recommend having Mathematica up and running, but I would not recommend it for typing notes 'on the fly'. IMO, it's always best to take handwritten notes (and research I've read backs this up). So likewise, if you only had a non-convertible tablet at your disposal, I'd recommend using it for taking handwritten notes (and recording audio, if possible/allowed).
After class you could type up and revise your notes in Mathematica as part of your study routine. However, the usefulness of this approach will IMO depend on the amount/type of mathematical content involved in the class. Explicit, well formed examples/problems work best, whereas purely symbolic examples/problems can lead to headaches rather quickly (depending on what your trying to accomplish and how good you are in Mathematica).
Whatever you choose, don't let tools disrupt your workflow or derail you from what you actually need to accomplish. (Mathematica can be a blessing or a curse, depending on your level of expertise and your ability to stay on task. I've lost many an hour bouncing around the documentation center, playing, etc...)