For those looking for instant gratification and tl;dr:
Now for what I came here for:
Welcome and hello fellow member of hell.
Glad you found/decided to join us here. As for the debate on your list of possible cars, I think whichever one you decide to go with will give you what you are wanting to get because each one has their individual pro's/con's
What I will say is that don't count out the 370Z on handling or because of its weight. For a car over 3k pounds, it handles extremely sharp. And that's stock... just wait and see once (if you buy one) how much better and even more responsive it would be with a few mods. I've put Abby through several canyons in SoCal and have been extremely impressed with it's responsiveness. Given its not an almost 6 figure priced car, I don't expect it to be 'the greatest handling car in the world' but it definately can snap your neck if you want it to.
Now assuming you do decide to purchase a Z...
The qualities you admire in the Lotus and the S2k can both be adapted to the Z with allowing you to drop it almost onto the ground if you want depending on which brand of suspension producs you go with. And as you know driving around in phoenix, lower isn't always better. I have a 7AT myself and I will agree with you, in traffic here it's a godsend. Maybe some of the die hard sports car fanatics out there will flame because you didn't get the 6MT but don't worry. They're just jealous our tranny shifts faster than they do.
I too have peered into the thought of auto-crossing with this car, but need to get a few more mods knocked out and get some better tires first. If you stay here in Phx, expect to get about 15k good miles out of the stock tires before you'll be wanting to replace them. If you keep it as a DD only and don't do any long trips, you might be able to strech that to 20k. I highly recommend (unless you plan on going with a full intake like the Stillens or Injens) getting the K&N drop in filters cause they will need cleaning...
Often.
If you do decide that a Z is what you want, and a 370 is what you want, check out the Private Classifieds here on the forum so you can help give a good car a good home. If you want a new one, PM me and I can give you a list of the local dealers to go to/avoid. I've had experience with 95% of them so I can help you out with that. If a 370 is out of your price range new/used, there's nothing wrong with getting a 350 and having fun with that. the good part with that is the fact that parts will be a lot cheaper.
If you have any questions or anything let me know and I can hopefully point you in the right direction locally.