mmm, dropping for premium handling, in the dry and on perfect roads then yes.  In the wet road holding will decrease but its all a big trade off to be honest, I lowered one of mine (KONI dampers and springs) and thought it was awful, took the springs off and went back to std.  Premium handling?  get a 306 XSi/GTi6/Rallye, they do fall to bits though but are far more sorted than the Golf.  I've had both so I can compare.
8v will deinately be cheaper and spending a few bob will increase performance but not by much.  Apparently, yes they will get better with age so a few miles shouldn't be a worry so long as you get history with the car etc.  You could add the money you would spend ont he springs to your budget and just wait for an early Mk3 16v.
What about a late Mk2 16v?  Should get a decent one for your budget, look on here but for more realistic prices try ebay or the trader.  Also, how do you drive?  If you go for screaming away from the lights and regularly revving above 3500 rpm go the 16v route, if not give the 8v a try.  Pretty good round town and on the twisties, upto 40 mpg on a run (seen 42 on mine) cheaper insurance, but they do run out of steam as the revs rise above the 5000 mark.
In the early 90's Autocar did a test with the then new Mk3 8v Golf against the Escort RS2000 Mark 4 16v. On paper the escort whupped the Golf, on the test track doing acceleration times again the escort whupped the Golf. On the raod test section taking in all types of roads and conditions the Golf left the Escort by a considerable margin. There really is more to the 8v than the 0-60 times.
I liked them so much, I've had 4 of them so far.....