For anyone that wants a better understanding of orbits and orbiting, I suggest this simulator: http://orbit.medphys.ucl.ac.uk/
. You'll find that orbits aren't intutive.
Like I said before, only if you are have the power to decouple from gravity, gravity is going to control every aspect of orbiting. Each orbit--an altitude above the surface where a trajectory encircles the globe--has its own period and thus its own speed by which a spacecraft must travel at to retain that specific orbit. For example, in the ISS's orbit, that speed is around 17,500 mph, no matter what size the spacecraft is, or how much it masses. The Sputnik, the Soyuz, the Space Shuttle, the ISS, and even the fictional USS Enterprise will all travel at this speed in that orbit.
Increasing thrust changes the shape of the orbit. If you are in a circular orbit and fire the engines, you will put the ship into a elliptical orbit. This is usually done at pericenter (periapsis, perigee, ect.) because you get an gravitational boost "falling" from apocenter (apoapsis, apogee, ect.) thus saving fuel. To make an elliptical orbit round, you spin the ship around to face backward and burn the engines at apocenter. The ship is now at a higher orbit, which has a longer period and a slower speed. To get into a lower orbit, the opposite manuevers are performed. Orbital inclination can be changed by reorienting the ship (usually 90 degrees from its flight path (in pitch I believe)) and firing the engines. This does not result in changing the size of the orbit or increasing the speed to any noticable effect.
Science Fiction has mostly ignored orbital mechanics for the sake of the story, and had thus done a great disservice to the Sceince side of the fandom. I'm not going to speculate how Star Trek gets around this issue. I just simply suspend disbelief.
One of the few movies that shows an approach to a planet in a believable manner is Alien.