Travelling at near-light speed is indistinguishable from being at rest.
This is the principle of Galilean relativity, and is preserved under special relativity: there is no feasible experiment to determine whether you are stationary or moving at a constant velocity. So there are no practical problems that would occur simply from moving at near-light speed that wouldn't occur at rest, and vice-versa.
Since everything inside the ship is moving with the ship at the same speed (this is why you aren't flung backwards when you jump while on a moving train), neither the crew nor the fuel nor the communications will be affected: for them, the world will be exactly as it would be it were not moving at all. It's the world outside the ship that would appear to experience the odd effects of Lorentz contraction, time dilation, redshifting, and what-not: everything inside the ship is its own protected bubble. (Of course, someone outside the ship would claim it was really the ship itself experiencing these odd effects, and that's perfectly fine).
The only time engineering is required is to handle the following cases:
* Acceleration: This is the only time when frame invariance is relaxed. Deceleration will cause massive stresses on your ship building materials, depending on how quickly you want to come to an abrupt halt. You should anticipate long deceleration times, something your crew will have to take into account. Conversely, accelerating to light speed will also take a long time if you want to avoid enormous compression stress. This includes rotation. 947
A full treatment of what the world looks like for such rotating frames can be explored by examining the <PERSON> metric.
* Navigation: Your starboard computers will register large amounts of redshifting from nearby stars, which can skew your metrics of where you are or what you are dealing with if you're using Hubble's law. A correction factor must be applied to all of your sensors to account for this - this can be easily calculated by knowledge of the ship's velocity.
* Synchronisation with off-ship clocks: For the crew inside the ship, it will appear as if life outside the ship is moving at a much slower rate. As a consequence, significant discrepancies between clocks at the ship's port of arrival and the ship's internal clocks will occur. This affects messages sent to the ship and any attempt to synchronise with the world outside. Again, a correction factor can be calculated and employed but must be known in advance.
* Knowledge of ship velocity: While this is on the surface not hard to solve - just measure the velocity of things moving relative to the ship - the devil lies in the details. Objects moving relative to the ship have their own velocity prior to the ship's acceleration, which skews measurements. One way out is to use standard candles, which we already currently use to estimate distances - simply compare the luminous intensity from a standard candle at one second and the luminous intensity at another, and use it to work out the distance that has been travelled. From this you can work out velocity.
You may also want to consider general relativistic effects: a ship moving at that speed has an incredible amount of kinetic energy, and will thus exert a significant gravitational influence in its wake (assuming its mass is already sizable to begin with). You'd have to figure out a decent flight plan that doesn't leave too much damage behind. 947