G-crane
You won't have to put the generator in orbit permanently, but you'll want to avoid operating this generator on the planet surface ! Because of the short distance, it will have a devastating effect on surrounding matter. Pull your space ship up (G+), rather than pushing it (G-).
To prepare for lifting a ship into orbit, your handwavium generator could first lift itself, e.g. 50m above the ship's ceiling. Then move the ship under it.
When the G-crane is switched on, it will pull anything off the surface, that resides in its vicinity. Not only the ship. The ship will need some armour, because the weight of the matter will put pressure. The trick to minimize taking matter along: while the cargo accelerates upward, the generator should move up, along with it. While the generator elevates the space ship "hanging" under it, its influence on the planet surface will rapidly diminish (G force diminishes with square of altitude)
The first few minutes of the lifting process will cause near objects, sand, dust, water and atmosphere near the surface to move upward as well. The lifting will cause large amounts of matter to stick on the bottom of the ship. The force should be maintained, until the ship is far enough up in space, to prevent sticking matter from falling back too early. When the generator is switched off and your ship is in orbit, the material sticking to the ship will detach and burn up in the atmosphere.
It is still advisable to move the whole operation into flat, uninhabited territory like a salt lake. The initial move will cause a crater. Underways, a spontaneous low pressure area is formed under the ship. Strong local airflow could cause tornados to occur.. maybe other weather effects..
