before any suggestions are made, we need to know room size, shape and decor, and the equipment the speakers will be powered and sourced by. Another factor is the type of music.
I completely agree with the quote above. Audio is a system, with the room and the equipment working in more or less equal parts to create the final sound. Many speaker manufacturers "voice" their speakers to work particularly well in certain kinds of rooms. So it is very important to know as much about your room as possible so that we can recommend speakers that will work WITH your room to create the experience that you want!
But just to get things started:
Others, I'm sure, will disagree with me on this, but I prefer to ALWAYS use a subwoofer (preferably 2 or 4 subwoofers) and adhere to a 4th order cross-over at 80Hz. Many many people prefer to use "full-range" tower speakers when the use is for music only, but in my experience, room interaction with the bass rarely makes the Front L/R positions the best place for bass response. This is just me, but I MUCH prefer to always allow a subwoofer (or again, preferably 2 or 4 subwoofers) to handle the bass. That way, you can optimally place the subwoofer within your room.
The cross-over from the subwoofer to the speakers is a vital consideration. Many many people opt for Front speakers that have quite low bass extension and then also cross those speakers over to a subwoofer. The problem is that most receivers or pre/pros use a 4th order slope to roll off the high end of the subwoofer, but they use a 2nd order slope to roll off the low end of the speakers. If the speakers are naturally capable of playing quite low, that gentle 2nd order slope is going to result in too much bass coming from the speakers. Some people like this "warm" sound that results and feel that it makes everything sound "bigger". But I find that it often damages the clarity of the mid-bass and upper portion of the true bass and can sometimes (depending on the room) make things sound a bit "woolly".
So me, I am a fan of using speakers that naturally start to roll-off the bottom end right around 80Hz. These are often bookshelf sized speakers, but when mated with 1, 2 or 4 very capable subwoofers, the combined sound can be cleaner, more dynamic, better focused and far more likely to work well within your room.
I know the kind of sound that you are describing. It is a sound characteristic of speakers that have a gentle roll-off in the highest frequencies, but more importantly, have a gentle roll-off as you move further and further off axis. You are likely to appreciate speakers with a slightly enhanced mid-range - especially since you enjoy listening mostly at lower volume levels.
Fatigue does not actually come from there being too much high frequency energy. Many people believe that a "bright" speaker will always be fatiguing, but this is not true. A "bright" speaker simply has an enhanced treble. What is fatiguing is distortion and distortion is especially fatiguing if it happens to be in the high frequencies.
With your budget, you are VERY likely to come across speakers that use tweeters that distort. It's just a compromise that has to be made at lower price points. Less expensive tweeters generally produce more distortion and that's just the way things go
Anyways, add it all up and my recommendation would likely go towards a 2.1 system. Some people will think I'm crazy for not recommending some $1000/pair towers, but as I said, I always favor using a subwoofer and in your situation, I would opt for a nice $500-ish subwoofer set atop a $50 Auralex SubDude mated with some nice $500-ish/pair bookshelf speakers and I'm likely thinking Ascend Acoustics or RBH would be a top choice for your speakers with a nice HSU subwoofer - the detail and clarity over the entire frequency range would knock your socks off from whence you're coming
