I'd vote (if I were empowered to do so) for either Gothic or Proto-Germanic. Gothic because it was there in 300 A.D., before major waves of Eastern European and Asian Steppe nomads began to force the massive movements of people we see during the late Roman period and the Early Middle Ages. Proto-Germanic for the reasons listed by Somerled, although I wonder about pronunciation of it and I'd also be weary of it because of its lack of actual evidence, its more of a hypothetical creation of scholars as far as I know (although I may very well be wrong). Overall I think Gothic is the better choice. Anyway some good sites are:

http://www.ling.upenn.edu/~kurisuto/.../aa_texts.html

http://sps.k12.mo.us/khs/gmcling/gmc.htm

Northern Germanic tribes, epically the ones of what are today the Scandinavian countries probably spoke something at least somewhat different, but the earliest language I know of for them is Old Norse and that dates from the Viking period so as far as I know Gothic or Proto-Germanic is the best this mod could hope to give them as well.