My experience of straight "track days" rather than schools is that even in the novice group, you get a lot of testosterone, varying abilities and while there are instructors on hand to give a bit of advice and show you the lines, it might not be the best experience for a new rider on a new bike who is looking for more focused, in-depth training that he can transfer to the road. Especially if you get nerfed on a corner by someone trying too hard. Definitely agree though that some advanced training is a good shout - and 'track-based' might make it more fun than the road-based training, especially for cornering techniques.
For an ongoing training programme that includes all the things the OP lists, I would heartily recommend something like the IAM or RoSPA. Or Rapid maybe, but I think the first 2 options give you a lot of time for your money. This could also be considered in addition to some track based training if it doesn't scream "birthday present".