Best speaker for songs like Heart - Alone

Yes you need speakers that can "pressurize" the room in the bass and the corresponding amp to dive them to their max effortlessly. The specific setup needed and associated cost will depend largely on room size assuming nothing too out of the ordinary about the room.

I just listened to that song, both the original and the digitally remastered. It is a tad bright and definately lacks bass and "punch". It sounded fine at moderate to low listening levels. My advice is to get a subwoofer or eq; some way to adjust the bass would help you out. I wouldn't ever use just one song to assess a stereo and like others have said, in order to build a stereo to make that one song sound good, you'll be comprimising the sound on most other songs.

Thanks for some suggestions folks! I have not got many specific recommendations of speakers and amp. So I hope for more suggestions what to check out!
It's more important for me to compromise, it's not so important that fantastic recordings sounds fantastic. A fantastic recording can sound "great" in my ears as long as bad recordings sounds "good".
Is it so difficult to find a system that plays (fexample) this song in a good way?

Given your responses, Rockpanther, this may be one of the few times in my life I would suggest an older used speaker, despite your desire for new. If you go new, with your budget you will likely sacrifice bass extension, which I can't see you enjoying. An older, very capable floor standing speaker might also be warmer; I'm thinking of Vandersteen 2CE or similar, which I owned long ago. These, and other Vandersteen 1, 2 or 3 series earlier speakers can be found in abundance, they have very respectable sound, and will not be fatiguing/harsh. You can also afford them if you don't have thousands to throw around.

You may also wish to go hear a panel speaker, because they sound quite different and you may love what they do. But be careful, because they can sound a bit unforgiving in the high end. Usually you can work with the treble.
Magnepan is everywhere, so listen to one and you'll know if it's a flavor of sound you like. It is definitely worth your time to check it out. The bass is thinner with a panel speaker typically, but you can supplement it with a subwoofer and get plenty of boom. For your interests it may be a winning idea. :)

When i was starting out Vandersteen and Magnepan were two speakers I could afford and kept me satisfied... for a while. :)

Rock-

there are 2 paths to choose;
since the song is 80's Rock, you can go vintage and look into Infinity speakers- I suggest the Crescendo series.
Or, you can buy newer designed loudspeakers like my reference, Thiel. I suggest the CS 2.4 or CS 2.7.
These speakers are simply outdtanding- you can use solid-state / Tubed gear. Keep me posted & Happy Listening! JA