If authenticity is your cup of grog, there is no substitute for Stan Hugill, whose recordings can easily be had from his memorial website.

Hugill (1906-1992) learned his shanties at sea in the 1920s aboard the last square-rigged British and German commercial sailing vessels. One of the last of the genuine shantymen, he was in good voice to the end of his life and is fondly remembered by many Mudcatters.

If you'd prefer something little less authentic but more immediately listenable and closer in spirit than many recent recordings, try anything by The Shanty Crew, Johnny Collins, Stormalong John, or A. L. Lloyd & Ewan MacColl. There are more good shanty performers out there, some probably reading this, but to me those named are among the very best.