Hey, I'm 24 here, started with hi-fi at around 15 like you and started with klipsch speakers and a jolida tube amp.
The harsh highs are definitely the speakers. newish Klipsch speakers are lively good for what they are, but unfortunately the horns used in them are harsh in the highs.
Though upgrading the speakers would be great, you really do need to get a nice sounding CD player, too. Some of the ~$500ish used players are great - the jolida 100, music hall, ah tjoeb, there are plenty of good choices. I'd do that even before the speakers.
Also - do yourself a big favor and learn a lot about speaker positioning. There are some good resources in the audio asylum FAQ. For your music to have depth, you really need to have the speakers a good bit out from the back wall. Speaker placement and the room acoustics is the #1 most critical aspect of any system, much more important than any single component.
The gallos you are thinking of would be a fantastic choice, and there are many others. I think you would like von-schweikert too. Used VR4JRs can be found for less than 3 grand, definitely worth saving up for. Go to some high-end shops and listen to what they have to start learning what different technologies and methodologies sound like. In general, don't pay too much attention to hype around any one component or technology. For every opinion, there are 100 contradictory ones, and you need to find what works for you, not everyone else.
Dont spend too much money on cables. Though many will disagree with me on this, anything more than a couple hundred dollars is a rip off for any cable, UNLESS you're talking about a system with ultra resolution that is completely optimized in every other way. Every other component will have a significanly higher effect on your sound reproduction then cables. Don't waste your money on expensive power cables or other expensive cables. I don't know if you caught this, but in recent history, someone cut open a ~$400 JPS labs power cable to find a someone else's ~$20 cable inside. speaker placement is 10000% more important than any cable.
