I'd hope they create a wonderful new cast, but Fallout's always had recurring characters so...
I'd want more Legion. The Legion got shafted somewhat by New Vegas so it'd be fun to meet a few more of their characters and see them given greater depth. I actually think a character like Lanius has the makings of a great tragic figure, so I'd love to see him return. His foil in the Legion was Vulpes Inculta so I'd be all for that honey-voiced furry returning also. This is entirely if the sequel were set in Arizona though. If it were set in Wyoming, I'd love to see the Khans again. I love that they have their own story throughout the Fallout series and it's a shame that with going to the East Coast the series leaves them behind. In many ways their story is integral to the themes of the entire series. I'd love to see them being given more depth and characters.
With specific characters, it'd be nice to know where Goris has gone. I have this fanfiction in my head of him trying to breed more talking deathclaws to eventually dominate the overall deathclaw population (and thus save his race from their inevitable hunt into extinction) so as this hypothetical new game will probably never happen, I'm gonna say that's what I'd want to see him do. But he's from Fallout 2, not New Vegas...
It would be hilarious if Fantastic had somehow wrangled his way into a new setting. No matter what happens he always seems to come out on top, so it'd be funny if he were somehow working as an ambassador for the NCR or something. Maybe he's remembered as the hero for getting the power to HELIOS One working, and gets sent as a head scientist to a facility in Mexico or Wyoming.
I would be upset to see Arcade Gannon on the run, but it could make for an interesting storyline. If Arcade fights with the Enclave at the Battle of Hoover Dam, he gets pursued as a war criminal by the NCR. Considering that a lot of the Enclave are octogenarians, at some point they're going to die and leave Arcade on his own. I'd be interested to see what a radical with advanced power armour could do!
Tabitha and Rhonda. I don't have much to say about them. I just think they would be a fun duo to encounter.