For purely road use I think that the Avon CR500 is the best tyre you can run on a Caterham.
1. It is significantly lighter than any of the competition and that translates to a good ride quality. You don't get any tramlining with them.
2. It has ample dry grip and is one of the best in the wet - you can get better dry grip but this is only really relevant on track.
3. It wears well under road use - it will last longer than R888/A048R/etc.
The only downside is cost but, as you should get at least a year out of a set (unless you are doing intergalactic mileage), it's not a massive cost. In the past I have run CR500s for road and track and they have lasted well - and that is with 226 bhp.
Regarding use of trackday tyres (like the ZZR) in the wet, as long as you drive to the conditions they are fine. I have driven thousands of miles in all sorts of conditions on R888, A048R and Kumho Ecsta V70A all of which have very limited tread and none of which have caused major problems. Caterhams are crap in standing water whatever tyres you have - just take it easy. Most Caterhams don't venture out much in the wet anyway.
Yellow SL #32 - member of Drowned Rat Racing