Classic means First Class of classic means Giant Size X-men? Because I think the former will be a terrible mistake. One of the reasons the First Class did not get traction is that , for an phenomena that is supposed to affect the whole planet , every single x-men turns out to be white and american. Sure it can be reasoned:"No, Xavier just reached the ones near him" but anyway readers were completely uninterested in how uncanny they were.
The second Genesis portrays way better the surge of Homo Superior. Irish,Japanese,Canadian,Native American,Russian, Kenyan,German...now I really feel the X-Gene. Some people will rage ( and-I-don't-care-at-all) but the truth is X-Men succeed as a series when diversity was introduced.
So my ideal roster for the MCU would be kind of Claremont's: Cyclops, Grey, Wolverine, Colossus,Nightcrawler, Storm and Pryde.
And yeah I know your favourite X-Men is missing ( not you you...you in general)..."DUDE....you can't let X out!!! it's so cool!!" but this is gonna happen anyway. I'm a big fan of Sage and a) there's zero chance we see in her in the first batch ( or the 2nd or the 3rd..) b) the only depiction of her in TV/Movies is that abomination called "The Gifted"....so ...many will be missed.