I wouldn't wear a kneeboard myself and would be unhappy about a second person wearing one in the other seat. They are genaerally over-sized and could cause a control restriction in some circumstances, for example on sloping ground (take your instructors advice on this).
However, I do use a double width, folding A4 sized clipboard (from a stationery shop, nothing overpriced from an "aviation specialist"), which holds a PLOG sheet and A4 sheets of paper with relevant info for my flight, such as landing site photos and sections of 50,000 map for use when finding them. I also temporarily clip on the flimsy A5 pages from Jeppesen's etc. to keep them ready for use and stop them blowing on the floor between the yaw pedals at an inopportune moment.... The clipboard is placed well clear of the controls, either behind the other seat or alongside if it's not occupied.
A pad of "Post-it" notes or similar is extremely useful. The stick-on sheets can be used for book-marks (they won't fall out of your VFR guide) and for writing down frequencies and other information in advance; I often stick these onto the folded nav. chart.
A small torch is always useful, especially at this time of year. I have a small Maglite (2 AA type) converted to LEDs.
Sunglasses will be needed at some stage, certainly when you get to the navigation stage. Sitting squinting into sun for an hour is no fun and not a safe concept.
You will need a decent jacket; don't be fooled into buying a nylon one as sold in the aviation suppliers' catalogues - they are totally unsuitable for aviation.
I agree with Whirly here, best to buy stuff as and when you need it, rather than turning up on day one looking like Action Man (helicopter nerd version).
Good luck with your flying.