potential mustang owner

[Hammer]

Were there any signifigant changes in the transmission between 2000 and 2003, or is it probably just an aftermarket clutch?

2000 GTs have a Tremec-built T-45 while all Mustang GTs built after March 2001 have a Tremec 3650.

The car appeared to handle quite well, but I was wondering if anyone had any experience with after market shocks, springs, sway bars etc., and their improvement.

The Mustang is probably the most after-market supported vehicle as far as performance-based products go.
(The Honda Civic technically has more after-market parts, but I don't count stickers and Altezza taillights)

You can make it a drag strip terror, or just as easily eat people alive on a road course.

Its all in the parts you put in it.

Be advised, I'm not a handling guru, but some Eibach Pro-Kit "Street" springs, KYB shocks\struts, and sub-frame connectors are a good start.

Also remember that any time your car is lowered with performance springs, you'll need a set of caster\camber plates and offset bushings.

In my opinion, the most important part of the handling equation is where your car meets the road. My recommendations for affordable, decent lasting performance tires would be:
Firestone Firehawks or Goodyear Eagle HP Ultra Plus

Hope this helps...