I want to keep the core classes pretty basic and then have the various archetypes be filled out by modular subclass-y options (partly inspired by what I've heard of PF2, which I really ought to check out before I get too deep into this so I have more reference points to draw from; I should look into other RPGs as well for that matter) and also by D&D 4e (which I never played but did look at a lot before 5e released), and also the default assumption is a nonmagical setting.
Which brings me to the tentatively-named Soldier (specializes in combat; think Fighter), Technician (specializes in non-combat stuff; think Thief/Rogue), and Operator (specializes in support; think nonmagical Bard, or the 4e Warlord perhaps). Ideally every class should have something to do in and out of combat, not necessarily in every encounter (though the core rules ostensibly should cover what's not covered by what specific classes can do) but certainly enough to keep players from getting bored even if they're not in the spotlight due to the current situation not being catered to them.
Of the characters I've devised so far - bear in mind the core assumptions are based on the setting sorXa & co. are in - sorXa, Alex, and Selena would be Soldiers, Selena's unnamed gf (god I need to name her already) would probably be a Technician based on my current ideas for her, and Jos would be an Operator.
I also want to have a "mage" type class as an optional thing for alternate settings where magic or magic-like tech exists (the Xeno- games are an obvious point of reference with ether, but there's also the fact that apparently Ciel was originally drafted up as a secondary playable character in the MMZ series who summoned Cyber-ELFs like a mage, though that was scrapped obviously, but it's still something that sticks in my head as a neat idea); it'd need to be balanced with the rest of the system from the get-go, but the rest of the system would also need to function without it, which seems like a tall order.