I bought a 1998 TDI NB for my daughter and the oil looks like it needs changing (there was no sticker or other indication, but it looks bad to me). I have heard that synthetic is the way to go.

Any advice on oil and filters? It has over 120K miles.

Tdi's oil will look black 1 min after running the engine after an oil change so dont worry about color. change your oil every 5k miles and use vw oil filters. Aftermarket filters usually dont clean the oil as good and sometimes make the wrong oil pressure. Use synthetic oil because it helps clean the engine better than normal diesel oil does.