I think it would be best to attend a few, just as a spectator, at a local track and firstly suss out the organisational skills of the particular Track Day organiser. Some arrange different groups based on levels of experience, beginner, novice, expert - some just have open pit lanes. I have only done a few over the years (always at Oulton Park), and the best are one 'make' days - so you dont get the Subar-buishi heros trying to out do a Porsche on track.
I did do a novice only day via an Autocar offer, just a half day session with tuition - well worth it always. Plus remember if someone is behind you, generally that will mean they're faster - so let em go! Without being paranoid - keep an eye on your mirror, if two 'wanabes' are playing, give them plenty of room, and let them fall off together!
I believe (though I've never done one), that the airfield based track days are a good learning ground.
Try also going to watch a morning session - get a few passenger rides and you'll be able to gauge the level of circuit confidence that people have, and then book yourself in for the afternoon session at a reduced rate.
Some Insurance companies do offer Track Day cover from the outset - especially if it's arranged by an 'official' club. Otherwise, on the day cover can normally be arranged through your broker.
Also don't forget that your car will get a hammering on track - it's what it was built for, but do make sure that your brakes are in top condition - oil levels correct, without overfilling! Dumping oil in a long sweeping bend never goes down well with fellow attendees!
Do enjoy
Graham