Thrust can be measured in multiple ways. Relative to fuel consumption, or relative to raw power measured in a metric of measurement I forgot (I'm leaning towards Joules though). Edit: Nope, it's Newtons.
Acceleration is measured in G force, and depends on the thrust to weight ratio of the ship you're pushing. High G thrust is for faster acceleration. People, assuming they're all strapped into crash seats can take 5 G of acceleration for a little while if you REALLY need to use your DeltaV.
Basically everything in space is based on relative velocity. Once you stop accelerating, you don't have to deal with the forces of gravity that are related to the thrust. Ideally, the whole ship and everything in it accelerated with it, and didn't smash against the back of the vessel during the acceleration. Otherwise, everything is going with the ship and once you stop accelerating, you won't notice the difference in velocity.
If you do your insertion right, you shouldn't even need to do a burn to keep orbit around the planet, though that's generally pretty difficult to do.
Jump drives are a whole different can of worms though, but in theory, there is absolutely no "acceleration" as a result of a jump.