I am searching for a very good headset. I primary use it for listening to music but sometimes I like to play a game.
So it would be nice if it has 5.1. The price should be about 60-80€ -> 80$ - 100$
Assuming you don't want to go the headphones + lapel mic route that often promises better performance, the Steelseries Siberia v2 should fit the bill pretty well (http://www.headphoneinfo.com/content/SteelSeries-Siberia-V2-Over-ear-Gaming-Headset-Review/Sound-Quality.htm).
The actual headphones/headset should always be a 2.0 type - you don't have more than two ears, do you? Interfacing to surround mixes is then best provided by headphone processing (Dolby Headphone, CMSS3D and the like). So-called "real" 5.1 units with 3 drivers per side tend to be a lot less effective and usually quite bad-sounding for the price.