Luke - Don't worry about tyres or changing anything on the car. Likely it will know its own way round the circuit anyway! (whichever one you choose). Best book some instruction. I used to book 2 for a whole day especially if I didn't know the circuit - one in the morning to help find your way around and another in the afternoon to refine things. One thing I would add is that several circuits do 'evening' sessions, which are shorter and cheaper. Not as much track time admittedly, but less intense than a full day. And finally, I always avoided having 'one last blast' at the end of the day. It can be asking for trouble if you're getting tired, so pack up and go home in one piece rather than do another 20 mins and invite trouble.
Would agree about avoiding Cadwell until you've done a few. I always found it took a long time to learn. Donny is good, as is Anglesey (often wettish there though, but a great circuit). Blyton is good and not much to hit!
Hartley
Photo taken at Croft (another good circuit!)