There are no special requirements to take a car on a trackday. There is no scrutineering of your car, it just has to be roadworthy and not leaking any fluids. You will also need to provide a full driving license on the day.
It's best to ensure your car's servicing is up to date, you have a decent (3mm or more, ideally) of tread and a decent amount of meet on your brakepads (esp fronts). I recommend you take a spare set of brakepads for the front, just in case. We can help you (if you need it) to change those out in 30 mins or less as we'll all have the tools required
Oh, and take some engine oil. The OMP goes into overdrive on a trackday and you could use as much as a litre of oil
You will need long sleeved clothing which covers arms and legs, although sometimes, in a covered car, the organisers allow sleeveless tops.
Helmets are compulsory (open face is fine in a covered car). These can be hired on the day if needed (usually about £10), but can be purchased from about £30 online. Good helmets start at about £120 and will have will some form of official motorsport approval (usually "Snell"). Helmets are NOT checked, but it's your head, so don't skimp! I can advise further if needed.
There will be a compulsory safety briefing at the start of the day, which will explain all you need to know about being out on track. There will also be "sighting laps", in which you will drive in your own car in a line of cars behind a pace car at the start of the day's proceedings so you can get to know the track layout and conditions, plus the locations of the marshals' posts.
I, and others, will be more than happy to take you out as a passenger to show you the ropes at the start of the day if you need it. Also happy to come out as a passenger with you. Tuition from professional drivers will be available on the day for about £25 (for about 20 minutes) and will be well worth it for someone new to trackdays.
I hope you can make it, there are 15 of us currently booked in, so you'll be in good company and we're happy to offer any help you might need.