Hello Ivan,
Pairing the Pioneer 575 with those Logitech speakers is like having a Mercedes with a Yugo engine
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Sure it will be ok, but it could SOOO much better.
The speakers will not be up to the task of quality music playback. Maybe movies, but just maybe. First, those Logitech's are designed for near-field operation - you have to be a meter away from them to work more or less ok; I have a small 2.1 Logitech system in my study and it's really crappy. It works for games & background music while you're working on the computer but is not Hi-Fi.
Unless you absolutely need DVD-Audio or SACD (there are very limited releases in those formats as of yet), I would suggest you go for a cheaper DVD player such as the Pioneer DV-366. The DV-575 has a built-in Dolby decoder as well - you won't need it if you have a receiver. Also, if video quality is not very important to you, but music quality is - you can get a even cheaper DVD player. If you use a digital connection to your receiver it makes very little difference what player you use because the actual signal processing happens inside your receiver.
Have a look at the Yamaha RX-V350 and RX-V450 models - you need a decent receiver, it's a must. Self-powered PC speakers will not work if you have any expectations of good sounding music. I am told that the entry-level Pioneer amps (D514/D714/D814) are not as good as the competing Yamaha products. Don't go for high power, most of those amps don't push more than 70-80 watts per channel anyway, regardless of what it says on the box.
Then have a look at the Wharfedale Diamond 8 series. Buy a 8.Centre and two 8.1 now. The front three speakers are the most important. Save for a couple of months and then buy the 8.4 towers - you can put them at the front and move the 8.1's to the rear. You won't have a subwoofer but I promise you those Wharfedales will pump out more clean bass than the subwoofer from the Logitech system.
Try look for some second hand stuff - like
www.ebay.de, online vendors. Maybe ask someone who travels to UK/Germany to buy you something and bring it back. Might be cheaper this way.
Good luck!