So while Bullet is pretty featureful you can just use whatever it is you want. Implementing simple gravity is ridiculously easy. As in when you create a rigidbody by default it has gravity and will happily fall endlessly without a floor collision object (For my space game I had to make sure to use setGravity(Vector3f(0,0,0)) to stop gravity from dropping my ships through the floor).
To stop things like rotation look through the forums for examples like here: Lock Z axis - #13 by m4tx
Edit: Basically saying to just use Bullet. It’s fine and not that scary once you follow the tutorials.