Is Shell Rotella T6 5W-40 Synthetic oil a reasonable choice for my 2002 1.8 TDI

As long as it has a 505.00 rating it should be fine.

While it is an extremely good oil, no T6 is not 505.00 rated. The Quaker State that is rated as such used to be a dealer only thing, but there are others such as motul lubromoly, total that are imported and readily available (cheaper). Also any 507 rated oil would be fine, but more expensive if you can't find the above in 505. I know ID parts has the right oil. Tempting as it may be, it does do harm to use the wrong oil in the long run, usually the cam wears excessively. enjoy your beetle, the TDI is a great motor.