*WARNING: WHILE I DO MY BEST TO AVOID SPOILERS, THIS ARTICLE IS BEST RESERVED FOR THOSE WHO HAVE SEEN FIRST CLASS ALREADY*
I saw X-Men: First Class in theaters, and I loved it! While I enjoyed the whole pre-Avengers Marvel films (CA:TFA and Thor) it was nice to see a Marvel story that wasn't too focused on setting up a future film; and while I believe that First Class could exist on its own as a stand-alone prequel/reboot, I think that there are still more stories to tell and a lot of gaps that haven't been explained between X-Men: First Class and X-Men.
This is not based on any rumors or rumblings, this is strictly a nerd who loves to think out loud :)
#1 Make Beast...Beast!

I loved almost all of the characters from First Class, except for Angel, Mystique, and Beast; and only two of them had valid character-related reasons for me not liking them. Angel and Mystique have reasons for having insecurities; they have very physical and difficult to hide powers. Beast on the otherhand, is mainly in his human form, and even then the film paints him as this insecure person, Beast was never much of an aggressive type (The X-Men once tried to break him out of prison, and he refused on the grounds that he felt like the justice system needed to be followed through). I felt like Beast should've been more like Xavier throughout the film, and instead they grouped him into a general story theme that didn't work for him. I looked up Beast up and found this apphropriate phrase about him:
"Fighting his bestial instincts and fears of social rejection, the Beast dedicates his physical and mental gifts to the creation of a better world for man and mutant. He also has a witty sense of humor."
Like I said, I didn't feel that in First Class, now they could just chalk this up to Beast having just joined this team, and he's nervous, whatever. In the next film, they should at least push to have beast be more like he's been in the comics and even the 90's animated show.
#2 Keep The Focus on Magneto
I don't know about everyone else, but I'm going ahead and saying that the filmmakers were smart to focus in on Erik, while arguably the story is about Erik and Charles eventually growing apart, it's not without the history of Erik that the story could be as strong as it is.
Many times throughout the film, I felt an instinctual draw to Erik as he's the most human of the two, Charles is often times chasing girls or trying to be the leader of the group, so i think with a character like that, you tend to become alienated yourself. Keeping Erik as the lead was smart as it connects us to the film.
Now, arguably Charles is more modest at the end of First Class, but I think it's still worth keeping the attention on Erik. He grounds the film and makes it more worthwhile to see the anti-hero right the wrongs of the world.
#3 Don't Pit The Brotherhood against the X-Men...yet
Many might want to see the Brotherhood fight against the X-Men, but that's been done in three films already, its getting tired, and that's sort of why a reboot was needed in the first place.
Much like The Dark Knight, I wouldn't mind a First Class sequel dropping us into the daily lives of the X-Men as they maybe have to go stop a plot by Magneto, but don't make it the focus of the story, maybe have the two work together once more, albeit with more tension within the group.
Here's where I suggest villains, surely you'll want to hear this.
My first choice is the Shadow King, he has a past with Xavier, and made him the peaceful man that we all know him as. One of the great things about the Shadow King is that he's a simple villain, he wants to conquer the world, and while Shaw made for a great villain to fight Erik, I think that the Shadow King could make a great threat for Charles. The Shadow King could also introduce a great way to bring Storm into the mix, and after watching Riptide from the first film, I kind of want to see Matt Vaughn tackle Storm in his new universe.

Proteus would also make for a strong candidate, he ties together to both Moira and Charles, and you could always have Moira ask Charles for a favor in terms of helping Moira confront a son who's been shunned his whole life. Charles and Erik argue throughout the first film about what role humans have when it comes to the oncoming evolution, and yet it'd be great for both to be sidetracked by Proteus, a villain that presents a challenge to both human and mutants.
Finally, Humanity. Why Humanity? Well they almost got destroyed by Magneto in the first film, and I'm sure they will have been assaulted by Magneto a few more times, have them respond with the Sentinals. A villain that has been grossly overlooked in FIVE X-Men films. I think it's about damn time guys.
#4 Introduce a limited number of new mutants
I already mentioned Storm, I think 1-2 new characters would be fine. Obviously, if they went the Shadow King route then Storm would be a must. If they did a Humanity angle, I could see Scott being introduced (Maybe Jean as well, give Scott someone to flirt with) if they went with Proteus, I'd love to see Colossus, like just make him a tank! Make him nearly unstoppable.
Finally, #5 More Great Cameos
Drop in Mr. Sinister and Apocalypse for a 3rd and final installment.