Seeing as I'm
from this century, and I presume that I'd have my family with me, I'd first like for us to spend a few years vacationing as complete wastes of space

, taking in the sights on Earth, Vulcan, etc. During this time, we'd also be taking advantage of 24th century medical technology to get healthy and fit. If or when we got bored with that, we'd either set up some sort of business in the DS9 Promenade and meet Gamma Quadrant aliens that way, or maybe even get hold of our own ship and go exploring/trading in that direction.
I voted DS9/Defiant, since that's the closest option. But just because we're transported to the future doesn't make me more likely to run off from my family. And families on Starfleet ships is just a dumb idea, IMO.
If I were flung forward alone, I'd try
continuously to get back. Preferably, with a copy of the 2050 sports almanac.
