Ok, this is my take on that:
Basically, a big part of this I call utterly crap (sorry for beeing that harsh). Especially all the "traditionals". Music that is several thousands of years old, or even older. I mean, we (the humans) built a spaceship and then put some of the most ancient music on it. Not even sure that some of this can be called music. It is like we take a clump of clay and say: "Look - this is where we came from!"
Maybe NASA did this to protect us. It seems as this record ties to tell the aliens: "If you want to be happy, stay away!" 
To be fair, not everything is that bad, let's talk about the positives:
Bach - Brandenburg no 2. Normally I am not a fan a Bach, knowing he is considered as the greatest composer of all time. I admit, he is one of those who layed a foundation for later composers. This specific piece may be an exception and is one of the more enjoyable pieces of Bach, unlike the other two Bachs on this record.
Mozart - Queen of the night. Normally I don't like this kind of voice, but I must admit this nightingale part has something. But still - this voice may be remarkable, but it is not very representative how we humans normally sound.
Beethovens 5th. Okay - this is some really good piece of our planets music and it would be a bummer, if NASA had not added this one.
Louis Armstrong - Melancholy Blues. It has Melancholy in the name. Questions? And still, it belongs to the top 10% of the entire record.
Blind Willie Johnson - Dark was the night. Some bluesy tones, but with a very depressing mood. Okay, blues is depressing in general. And this is my guess why there are 2 of them on this record. Did I mention, the entire selection has a quite depressing mood?
Chuck Berry - Johnny B Goode. Finally one song with drive. One single piece that can be called "modern" back to these days. Maybe this is the appempt to telling the aliens we are not species made of entirely wet blankets. I still wonder how this one made it to the record. Maybe one of the NASA deciders was drunk or he lost a bet.