1. Transporter
While warp drive would be fun, transporters are the ultimate Star Trek gadget. Beaming effortlessly from place to place is incomparable. You want to visit Antarctica for a few moments - put on your winter coat, step into your transporter and materialize away. Visit a hundred different exotic places in seconds. While you would need a controller to send you to and from your destination, you could pretty much travel wherever you pleased. Despite the ease of travel, I'd have the constant fear that, in the process of beaming, I wouldn't materialize the same way or some of my particular matter would be lost forever in the transporter. I don't doubt that some of the Enterprise crew lost a bit of themselves beaming from planet to planet.