Which world would you visit?
OK, you may be thinking you'd never visit any of those "worlds" if you could. Even putting aside their disastrous ending, they're really expensive (at least in today's dollars) and have plenty of flaws pointed out here on IMDb. But this hypothetical is about preferences among the three romanticized settings. Which appeals to you most?
I suspect that the most popular answer would be Western World, partly for its relative recency, partly for all the TV and movie references to be made, and partly because it's what we see the most in this movie. Medieval World might give it a run for its money, considering all the Renaissance fairs. Then again, maybe that's a reason not to bother with Medieval World: It's little more than a renfair with robots.
But my vote is for Roman World. It's the most exotic. The one I'm most likely to learn from, tho I'd make sure to fact-check later. The one with the most comfortable-looking clothing. And the one with the best reputation for hygiene.