if you put 19's on yes it will be a very stiff ride .... However you should not have any rubbing with the stock setup. the wheel wells are very big, and on 2000-2002 they are even bigger. However I do recommend you drop it as it will sit pretty high on 18's.
If you put on just springs on your Z your shocks will last you no more then a year, its recommend you change both at the same time, but if it's low miles and you wanna get the most out of your current shocks then just ridem out and make sure to have a set of bilistens laying around ...
19s is the absolute biggest you should go and if you drop the car it will fill in the entire wheel well. If you want some more information check out the Z3 section at bimmerforums.com, They have some Z guru's on there.
Anyway good luck and make sure to post pictures when your done with it.
**i'm riding on 18's by the way.