I'm on ZII Star Specs, cost me the same as the ZI you're looking at in OEM size.
They are louder (they throw rocks n' junk into the fender liners) and less fuel efficient than the OEM tires are, any tire that is a serious upgrade in grip will have similar results. However they have been very durable for my AutoX and track days and I have no regrets choosing them but that was my goal going in.
It will be next to impossible to find tires that are grippier AND longer lasting than the Primacy HP's, I got 30k miles out of them with 2x track days and in hindsight they were waiting for more, I jumped away from them too soon.
As it sounds like you are not interested in beating the piss out of these tires at an HPDE or AutoX I'd think you wouldn't be happy with the 200 treadwear tires designed for competition use, the PSS gets lots of love but I have come across people who have had them not survive serious lapping, they would likely be a good choice for you since that isn't a priority. Continental Extreme DW's mentioned above are in a similar vein and would likely also serve you well.
If you want cheap I know some people that love Sumitomo HTR Z III, ~$80/each so you can start getting an idea of what's out there. General consensus is that they're pretty much obliterated after about 4x Track Days for an amateur driver so if you plan on doing more than that it might be a loosing prospect.
http://www.tirerack.com/tires/tires....omCompare1=yes
Sounds like you're in the market for a solid 'Max Performance Summer Tire' all you can do is read a bunch and make a best guess.