If you don't mind jumping in almost exactly at the middle of a series, thereby spoiling some earlier storylines for yourself, you could do worse than starting with Treason's Harbour, I think. It's got a lot of the elements that make the series great, it's pretty easy to follow the action without a lot of prior knowledge, and it's not overburdened with nautical talk.
Just for the record, some of the elements that make the series great are:
- Daring escapes from the French (boo, the French)!
- Illicit liaisons with ladies!
- Stephen looking and smelling like some kind of mythical hermit (an honest-to-god plot point)!
- Sea battles (although there aren't the lengthy and detailed descriptions of nail-biting close actions in this one, but there's enough to let you know if it's your thing or not)!
- That scrub Harte showing away!
- Jack being an excellent commander, a discreet and loyal friend, and freakishly strong!
- Killick complaining!
- The Surprise!
I could go on. And no doubt I will, the next time I see you.