The Legion stories would obviously take place 1000 years in the future. That is part of what defines the Legion, after all.
I would like for writers to also really think about what time travel means. The recent Legion Lost series started out with the Legionnaires 'arriving too late' for something, which was just ****ing ridiculous. A time machine never arrives late. Or early. It arrives exactly when it means to. (saith Gandalf)
Similarly, 1000 years in the future doesn't necessarily mean that every single day that is passing in the 21st century is matched by a day passing in the Legion continuity. It's not an alternate universe that's running parallel to the present, but *exactly* 1000 years later, and there's literally *nothing* (barring Iron Curtains of Time and / or time travel mishaps...) preventing, say, Brainiac 5 from going back in time to visit Kara Zor-El *before she died.*
Or various Legionnaires yanking Mon-El out of Zone storage *hundreds of times* over the 1000 years he was supposedly trapped in there, and then adjusting his memories afterwards, so that, when he finally is decanted, he's got a lead cure *because they've been inoculating him over centuries.* (and he's surprisingly sane, for 1000 years of PTSD, because he's actually spent entire *centuries* out and about, doing stuff he no longer remembers, because his brain literally cannot brain that much brainage and something had to go!)
So why not postulate that, early in its existence, the three founders went back (at various times) to the 20th century *of their universe* and recruited Superboy, Supergirl, Lana Lang (Insect Queen), honorary members Jimmy Olsen and Pete Ross, and various Super-pets?
In fact, we can just say that the Legion operates on Earth-W, along with all those characters above, leaving the group's entire history intact. The reboot and threeboot teams can be considered to be alternate earth versions of the Legions, just as the JSA was considered an alternate earth analog to the JLA back in the Silver Age.
Seems *completely* reasonable that if a multiverse can have alternate futures, not set in stone, then it can also have *multiple pasts,* because that river that is time floweth both ways.
As to where any new series would start, I would say pick up the story just before the Crisis on Infinite Earths. Make sure both Superboy and Supergirl (as Brainy's love interest, of course), make occasional appearances, and, if there are any trips to the past, make sure they take place in the world that Mort Weisinger gave us.
Sounds good to me.
Pick literally anything, and it's probably been destroyed, doesn't currently exist in the nu52, or does and is about to be destroyed *four or five times* in the next decade or so of serial storytelling.
And so, it's *literally* meaningless what's going on in the 21st century, to the stories set in the 31st century.
'You can't have this story set on Tamaran! It was destroyed in the blahedy-blah of blah!' 'And now it's back. Was it rebuilt? Is it another planet entirely named Tamaran? Did some time shenanigans occur and undo it's destruction? I don't even care. It's been a thousand years. It was destroyed *twice* in the first ten years of it's DC existence. Following that progression, it's been destroyed *two hundred times!* in the last millennium. I guess we caught it between destructions!'