Not neccesary to have insurance, but you risk having an expensive repair if anything happens. Insurance will most likely cover your car and repairs to the circuit (I.E Barriers)
I'm guessing by PSI you mean tyre pressures, I don't think that will be the main thing to think about on your first track day but checking to ensure it is around 33Psi at the front and 31 at the back while the car is cooling down.
A more likely thi g to thi nk about is brakes, these will be the first thing to give you headaches on a track day, very good fluid with a high boiling point is a easy start, and maybe new pads to help fend off fade for an extra lap or two.
If it is something you are thinking of doing again or if you already have one, a helmet might also be a worthwhile investment. Although rented ones should be more than good enough for your first time out.
Most of all enjoy yourself, don't try racing more experienced track dayers, even if they are in a 'slower' car as they will most likely be able to catch/ overtake you easily and no-one will want to be stuck behind the guy who wont move over and learn your car/ best lines rather than how fast you can go into a corner. You still want to be able to drive your car away after!
(No expert myself as I am doing my second trackday september 12th, these are things I picked up on from my first trackday at Silverstone in Feb)
Hope that helps!