There is not much equipment that you need to begin flight training. You already know about the headset (sometimes the aero club you are training with will provide headsets) and the most important thing of course is your logbook, where you will record and log in every flight that you do.
That is almost all that you need. Some aero clubs/training providers prefer if their students have a Student Record Book. This is just a plain and simple book that your instructor can write a detailed summary of your lesson so that you can have a read of it before your next lesson, and it is a good thing to look back on later on in life.
You will notice that instructors carry pens around all the time because they do a lot of writing (eg: tech logs, defect records, writing student records, signing things, logging in their flights) so having a pen handy would probably help too.
And that is basically all the basic equipment you need. If their is anything else your aero club or flight training provider will most likely have it either available to you, or available to purchase.
Godd luck as well with your flight training, and enjoy it, because flying is probably the best thing you could do.