Popular opinion is the 2003 models.
-last year of the ALH Engine
-best fuel economy (autos get about 10 mpg less than 5-speeds)
-cheaper performance upgrades than the later Pump Duse (PD) engines.
-more options for performance upgrades
-
some previous issues with the rest of the car have been addressed.
Later PD engines are a common rail setup. The injectors are operated off of the cam. So even a simple injector upgrade is pretty expensive. Also, there's a specific engine oil you have to run to prevent premature cam wear.
Here's a cutaway of a PD motor:
Important things to know:
Ask for maintenance records!
-Timing Belt
needs to be changed close to 100K. (Preferably closer to 80K for safety).
-Intake Manifold will clog up and needs to be cleaned. There are a few steps that can be done to slow down, or prevent this from happening (i.e. turning down the duty cycle on the EGR, or simply removing the EGR altogether). Some people setup a catch can for the PCV, to catch any oil mist. I decided against it, as there tends to be moisture in the setup which can freeze in winter months.
Here's my Clogged intake thread:
Intake Flow Problems
Automatics tend to have a more problems with their turbos. Being a variable vein turbo, the veins tend not to be "exercised" as much as the 5-speeds, so they can get carbon built up. This causes poor boost performance.
Even stock cars can have Boost Spike issues. The veins cannot open fast enough at WOT to release the excess pressure. Usually you are OK until you start doing any mods. Then you'll need to get yourself a manual boost controller to chop off the spike.
With proper care and maintenance people are getting insane mileage on these things. Easily 300K +.
There's much more to them, but these are just some of the highlights.
General FAQ
TDI FAQ
Again, these are opinions. As we know opinions vary from person to person, but I can attest to the 2003s since I bought one off the lot and have put 120K on mine.
Feel free to contact me with any specific questions. Good luck TDI Huntin'

"When you want to be a somebody; you drive a new car...When you know who you are; you drive an old car."