Are meteorites igneous, sedimentary or metamorphic rocks? Are meteorites igneous, sedimentary or metamorphic rocks?
Or do we need a new method of rock classification for them?
 A: The heat of atmospheric reentry and the sudden impact of, um, impact, certainly metamorphosize the minerals in a meteorite. That's a whole fascinating branch of geology. Before the metamorphosis, though, I don't think either of the other terms fit, unless you're talking about a meteor that has already been processed through a large body as lava and ejected via impact.  Sedimentary might be closer, considering that asteroids do sort of aggregate together over geologic time, and there might be some volatiles involved, even some liquid H2O, if it gets big enough to heat up. Rocky, iron, and nickel meteorites might have different enough biographies that they could be different.
A: ["The heat of atmospheric reentry and the sudden impact of, um, impact, certainly metamorphosize the minerals in a meteorite."]  -- 
Not necessarily, only the surface would be affected (particularly on a large object), as while the meteorite becomes very hot on entry to our atmosphere, this time is relatively brief due to the high speed.  In addition, the object itself is very very cold. So while the outer surface is undoubtedly "somewhat scorched, the internal structure "should" be relatively pristine.  On examination of the interior, it should be possible to determine the origin (either accretion, ejection, or some other origin) for the meteorite.
Trouble is for the most part, collectors of meteorites are hesitant to allow the meteor to be cut in half or otherwise damaged.  So the question continues to exist.
A: A meteorite, is simply a rock. 
So yes A meteorite may be sedimentary but that requires a parent body that can create sediments.
A quick google search should show several examples of where sedimentary meteorites may have popped up but were not properly identified for several reasons.
I have been following a reddit post where the poster swears up and down the crust on his sandstone is just that, but unfortunately when it comes to sandstone without close analysis it's pretty difficult to say for sure whether or not it is.
It could very likely be weathering rind, and this is just a recent example of someone facing difficulty with a possible sed type... which in my opinion IS a huge deal.
A: Iron meteorites are thought to be from an asteroid or planet’s core- having once been molten, so they are closer to igneous. Though, since they were not necessarily brought to the surface by a volcano, or mixed with oxygen, their internal structure will not look like a lava rock.
Pallasites (stony-iron) have cooler mantle material (chondrites) mixed into a metal matrix, and are fused with the metal, so they might be considered metamorphic-like. But, again, not necessarily brought to the surface by volcanism.
Stony meteorites could have some outer crust characteristics, maybe even evidence of once flowing water (sedimentary rocks need water to form), so a meteorite could potentially have characteristics of sediment formed on the world it originated, but I would hypothesize that much of the evidence of the lighter materials would be obliterated during descent or upon impact. Most of what survives entry is going to be of the denser variety.
So (to answer the question), before these rocks entered our atmosphere they could have been any of those 3 forms, just like on Earth, but once they travel through the atmosphere they gain characteristics that classify them as meteorites, like a layer of fusion crust, or a “thumbprint in clay” look called: regmaglypts.
Note: these characteristics (like fusion crust) can wear away over time. Iron will degrade into iron shale and then the rock will appear to have layers like sediment. The only way to tell that the rock had space origin would be to analyze its composition and compare it to what is known of Earth’s geology.
Some obvious tells: Pallasites were probably formed from a collision between various molten materials of different temperature regions (like an asteroid with a molten core colliding with a comet). Since Earth is still intact, if you find a Pallasite-like rock (large olivine crystals embedded in an iron-nickel matrix) it is likely from space. Or if you find a natural rock of iron-nickel that has a criss-crossed metal matrix inside, it has also likely come from space.
Collectors have to be careful that they aren’t buying slag (a man-made by-product of the metals industry). It can often look like a meteorite on the outside.
So, sometimes the only way to tell for sure that a rock is really a meteorite is to look inside. This is a very common thing to do and is called “windowing”. Many collectors prefer a cut stone for verification- and for its beauty (the inside is usually amazing, so why not have both).
