I think this depends on how far you are willing to go to get good sound. If you are considering the HD600, then I must assume you are willing to go to considerable lengths to get good sound. I've heard a teac minisystem at goodguys, I don't know how similar it is to the one you have. I don't know the model number of the one I heard, but I think it was a fairly small minisystem with a aluminum face plate and wood finish on the speakers. If yours is anything like the headphone output on that, then in my opinion, it will be able to drive your HD600 better than a portable. It won't sound empty and hollow like the sound you will get straight out of your average portable. On the other hand, it's a terrible waste of a great set of cans because it won't sound like things
should sound either
Everything will sound much more full, balanced, and realistic on a better amp.
For good sound for little money, try an amp built by JMT or one of the other DIY people around here. The cmoy and meta42 are both relatively inexpensive. For the less discerning, I've heard that the cmoy will do you plenty good. Personally, I have a JMT built meta42 and am very pleased with the sound and build quality. There are also commercially available amps. The Airhead variants available on
www.headphone.com are popular, and the portacorda amps, available by Jan Meier's company (look at the index page of head-fi to see the link) are even more popular among the lower priced amps. The meta42 can potentially sound better than the Total Airhead and Portacorda, but it depends on how much money you put into it.
I have no experience with better amps, or even the two commercial amps I mentioned. The comparison between the meta42 and the porta/TAH is pure hearsay, albeit my sources are good (use the search function to find more info on these amps.)
This is of course all based on conjecture that the teac you have is similar to the teac I heard. One other option you might want to try is a cdplayer with a good headphone output.
Btw, your english is pretty good