Lids: Buy the one that fits and meets FIA regs. It may mean you end up spending £1000 instead of £300, or you may get lucky like me and find the £300 Sparco is a better fit than the £1k carbon Arai you wanted. Also never use bike kids in a car, they're designed for very different crashes and may not protect your head in an accident.
HANS: Up to you. If you have the budget then absolutely why not, even if someone at track thinks it's overkill you'll be very grateful for it if you need it. I'd buy a romper suit over a HANS first though, I think.
Harnesses/cages: Harnesses are fine with no cage, but only if done up properly tight else they can be more dangerous than a lap belt. Fine to use without a cage. Cages you need to be careful, as if your head could touch any part of it in a medium crash then you MUST wear a helmet at all times, including road use! This is why most people go for half cages than full cages, but it's almost overkill for a coupe on track unless you're running slicks. Harnesses I'd definitely do though, makes a huge difference to the driving experience.
I'd use DT to go and try everything on, then either haggle a discount when you're there (doable if buying a fair bit of kit) or just buy from any shop on the internet that looked half decent.