Vehicles items will beam down a vehicle from the players ship that alters the players physics and movement. Mechs and hoverbikes have already been designed and animated. Implementation on those has not yet started however. (From the Roadmap.)
Would many of the vehicles even fit? I guess you could get away with hoverbikes, but the mechs might be a bit of a squeeze.
For this works with spaceships is not that hard, Vehicles will require a ship upgrade that unlocks some Hangar! With the hanger unlocked you can have vehicles to store in your ship and take to your explorations in the planets! It's strange, the Space Station had that exact idea of store the vehicles and then when go explore, chose one, now with the personal spaceships, this must work differently.
I don't think shuttles need to be in the game. Transport to the planet's surface is done by teleporter.
What if you had to build/upgrade a hanger in your ship in order to store vehicles in your ship. That would help balance the game so you don't get vehicles too early in the game. (nice idea)
This could be handled simply. You could just have a device on your ship that you put materials into. After you collect the right materials, and customize your ride a bit in the menu (maybe paint it) you can have a vehicle beam down to the planet upon command. You could also buy vehicles and store them in the device, or somehow find vehicles, and beam them up. You could ALSO have a pad in your ground base for these to spawn, or, you could store them in a hangar. Think "Catch a Ride" from Borderlands, but tons of more customization.
Maybe just increase size of spaceship from small shuttle to huge dreadnought that can fit anything? Including army of mechs, tanks, fighters & etc...?