Aerodynamics is the study of gas flow around a rigid object. Zeiss explained that the density of interstellar gas is too low for this to be relevant. However, at velocities of just a few km/s, solid objects impacting a solid surface cause the impacted surface to behave as a liquid. That's 103-104 m/s. Recalling that $c$ is about 108 m/s, even traveling at a mere 0.1% of $c$ (about 105 m/s) will guarantee that you will impact some objects at well above the "liquefaction threshold". This is why there is no such thing as an "immovable object." No matter how big or dense you make something, there is something else which can be thrown at it with a velocity which will, at the least, cause the target object to dissociate. Black holes are the only exception (but throwing objects at them should cause them to move, nevertheless).
As others have noted, since you need to shield your ship in the direction of travel, you want to minimize the cross section. Since we presume the interior is pressurized for the survivability of the crew, a round-cross section provides the strongest containment shape (which is why airliners and submarines are mostly long round tubes). This is what leads us to a cylinder (not very sexy, I know). However, there is an important trade-off to be made. Tiny rocks in front of you are not the only hazard in space. The threat actually comes from all sides. Cosmic rays are also very dangerous to your crew, so you cannot simply make your ship a long, thin needle. There needs to be enough shielding mass on the sides to reduce cosmic radiation to a survivable level. So the ship should be long and narrow, but not too narrow.
The easiest way to change course is to turn off the main engine, rotate the ship to the desired vector, and turn on the main engine again. "But wings will save you from using RCS thruster fuel!" You actually don't need RCS thrusters to change orientation. You can do it purely mechanically, via gimballed gyroscopes, which is what the ISS does. There are limits to how much angular momentum can be altered, but since most of the time, your angular momentum should be zero (unless you are spinning for artificial gravity, in which case you have a whole bigger set of challenges), this accumulation should not normally be a problem. Even if you do need to make an attitude adjustment, the gyros should reduce your RCS fuel consumption dramatically.
Yes, the nose must be armored. But armor might not be enough. Star Trek has only a tenuous connection with real physics, but one concession to interstellar travel is the so-called navigational deflector. The closest thing you could make with real physics is a kind of internally generated magnetosphere. That would help divert charged particles, but wouldn't help so much with electrically/magnetically neutral ones. However, you could make everything charged by shooting everything in your path with a laser, producing enough energy to ionize everything about to hit you. It's questionable whether a ship could produce enough energy to actually deflect impactors at a significant fraction of $c$.
There was a relevant question about magnetic shields on the Space SE. But such a shield only protects against particles. The most dangerous threat is really gamma rays. The only reliable defense against these is a lot of mass. Theoretically, if you had a really good scintillator, you could down-convert the frequency of the gammas and harvest it as energy (to help power your magnetic shield, for instance). Possibly, the front armor plate could act as both a gamma scintillator and a particle shield for bits that make it through the magnetic shield, but it would probably need to be replaced periodically, because I think both uses will degrade it over time.
If you have a deflector laser for ionizing rocks, then the nose of your ship will be quite busy. The shield/scintillator will need to be opaque to gamma rays, but transparent to whatever frequency your deflector laser runs at (UV? you don't want the deflector to be too high-frequency, or it will go through the rocks instead of ionizing them). Some real-life gamma scintillators are transparent organic crystals. So it would be pretty cool if the nose of your ship was a big thick glass-looking crystal with a laser battery and PV array behind it. Food for thought.