When I browsing Amazon for speakers I see in the description specifications like maximum input power, Frequency response curve, Audio Sensitivity etc. Does the type of music you listen to factor into determining which ones to buy? Like personally I listen to soothing and pleasant music instead of high beats. Will this mean I should look for some specific parameters/specifications in the speakers for the best experience?
Ideally, you always want a system (speakers, amps, room, etc) that can accurately reproduce the complete frequency spectrum of human hearing (around 20Hz to 20kHz), but this is not always possible, so building a system that favors your musical taste is a good idea. Knowing where to make sacrifices and where to re-enforce can make a big difference.
For example, if you are mostly into simple guitar-voice Nueva Trova (a genre that features guitar and voice prominently, often exclusively), you might want to pass on a subwoofer and focus in the other ranges. Lowest guitar note is normally around 80Hz, the human voice is normally above 100Hz, and subwoofers normally reproduce frequencies bellow 80Hz, so a subwoofer here isn't doing a lot of work, it wouldn't make a huge difference.
In contrast, if you are mostly into electronic music genres, which normally have a lot going on bellow 80Hz, a subwoofer will make a huge difference (as in night and day difference).
Every part of an audio system (not only the speakers, but the amps, the room, your complete listening environment) has a characteristic sound. Some have more bass than others, some have more treble than others, some distort less than others, etc. Try to aim for a system that suits your musical preferences.
We are talking about frequencies here just to make a point, but the best way to decide which speakers to buy is to listen to them. Grab your favorite songs and test them through different speakers (any decent store will let you do this). They will not sound exactly the same in your living room, but it will get you a good idea of their character.
Every speaker or amplifier has a specific sound and therefore strengths and weaknesses regarding specific tracks or even genres. E.g. there could be speakers that play e-guitars very well or some that are good at the kick-bass of some sorts of electronic music. Especially in the lower price range it is difficult to get an "allrounder" that is decent at everything. You might even be able to break down your preferred music to some technical details. A reference curve of a speaker would be a good factor for that. This of course requires you to know which frequencies matter in your music.
So what should you look for if you want the best experience? Forget about the first paragraph of my answer! The most important factor is taste and feeling. A speaker might play your music very well in theory but still sound horrible to you. You can buy some 50,000$ sound system that is very highly rated and still end up not really liking it's sound. So stop browsing Amazon, pack some of your music, go to a store and listen :-)