As with Classic, a lot depends on what the objectives of the scenario are.
In most cases, I've used J. Edgars for speed/scouting, and Pattons for bricks of health to stick in a spot and say, "Try and kill me".
I'm still painting up my Kickstarter haul (bases first with color markings), and I don't know when I'll be making an Alpha Strike list again.
All that being said, I don't see most of their uses any different from what I'd use for Classic. If I'm not painting by ForcePack, I'd probably go with Warriors and LRM Carriers first. Warriors are in a good spot to see everyone on the board and spot so your LRM Carriers don't have to expose themselves to fire.
From there, if I'm going to use Infantry (Conventional or Battle Armor), get those Maxims painted so they have a ride.
After that I'd split it between Hover Strikers and Tracked Brawlers/Juggernauts to act as that middling force and fill up holes you might not want to use with Mechs.
Galleons would probably be last, honestly. The only good thing they can do is cheaply attract fire that might go to something else or slowly plink away at something that ignored it. They could scout through forest better than anything else on the Ground, but Warriors can do that more efficiently.