Please assume the following:
- structural integrity is not a problem, accelaration will not damage the ship/ the passengers
- There is a source of abundant energy on the ship, consider it enough for almost any purposes.
- FTL is not possible.
- All used technologies should be extrapolations of current technology or plausible inventions within the next millenium. Basically everything that does not break the current understanding of natures laws. And yes I am aware that 1. and 2. are breaking these, at least probably.
- Collision avoidance and all other problems with very high velocities can be neglected.
Under these conditions, what would be the fastest spaceship engine or the one with the quickest acceleration? What could bring that sleek ship up to a significant fraction of c and bring it to (relative) halt again?