If Fox is serious about making an X-Men TV show, the properties that immediately come to mind are New Mutants, X-Factor and Alpha Flight.
New Mutants since it's a high school drama where every few episodes a supervillain like Emplate would show up. It's also an excuse to see Mirage, Cannonball, Cypher, Surge, Dust, Prodigy, Hellion, Meltdown and Chamber. This is the most obvious property to develop.
The only reason why I can imagine a New Mutants show not being produced is because Jubilee is a hard character to make likable. The version from the animated series was a cross between Shadowcat and Meltdown who was Jubilee in name only. The character from the comics is this whiny, lazy little kid who once refused to eat lobster at a seafood restaurant to the waiter brought her Mcdonalds. It's hard to get an audience to relate.
X-Factor would also be good since it'll be about mutants who are tasked with hunting other mutants. If it were up to me, I'd draw from each incarnation. They work for Serval Industries (fourth) which is a government contractor utilizing mutant mercenaries (second) that hunts down rogue mutants and tries to reintegrate them back into society (first) and each story arc will revolve around whodunnits and really hook the audience from episode to episode.
X-Factor would naturally be able to combine the casts from the past and present since Layla Miller is a walking MacGuffin for time travel and alternate universes so it would be an excuse to bring back Havok, Gambit and Quicksilver from the 80s into the 2010s and then watch as they struggle with the future shock like Quicksilver learning that he has a much younger half-sister when Magneto fell in love with a much younger woman and Havok seeing his nephew all grown up alongside hearing that Banshee who was one of the original X-Men was murdered by his brother and his daughter is now out for vengeance. Layla is shocked that after bringing back the three former X-Men from the past, she's a living temporal paradox who technically never existed. None of them are surprised that Mystique hasn't aged a day.
X-Factor's present day roster would be Val Cooper, Mystique, Forge, Siryn, Multiple Man, Rictor, Polaris and Strong Guy who are caught up with four time travelers so there's already a really full cast that's way too large for a film. Also, Mystique this time around would use her human disguise most of the time, partially for budget and partially because that's how she looks when she interacts with Val.
Alpha Flight would be more of a show like MASH or JAG where it's all about military bureaucracy. As somebody who watches JAG, just because it's military doesn't mean that it needs to be all action and explosions. There's also room for storylines about the team bonding and running training exercises. With most of Marvel's team books, the characters get down time in between the crossover event comics and with the cast of Alpha Flight needing longer arcs than what a film can provide to develop things like James and Heather's romance and Jean-Paul learning to be a team player, Alpha Flight looks like it would be a really good show for Fox on primetime. Also, many of the members of the team lack energy projection so it saves on the budget in addition to Madison not suiting up as Box unless he's in the field. And Alpha Flight has the highest potential for cameos from Wolverine and Deadpool so there's star power from Jackman and Reynolds alongside name recognition.
I'd put New Mutants on Fox since it seems like it has the greatest commercial potential as a primetime TV show on a channel that nearly everyone has. X-Factor would be on FX since it works better as a cable show due to some of the edgier material like Rictor coming out of the closet and how he doesn't feel totally accepted despite being around other mutants since he's the only gay and only hispanic member of the team. This alongside the really convoluted plot lines and expansive cast makes this one of those shows like The Walking Dead, Game of Thrones or Battlestar Galactica that works best on a cable network since it would jive with most of the FX original series.
Alpha Flight would either be a streaming show on Amazon or Netflix or it would be used to get more people to subscribe to FXX. FXX just launched in Canada this month and Alpha Flight would be great for opening up that market and getting more Canadian subscribers along with making FXX more than just a lesser version of FX.