The power FETs and resistors are now in place and it runs perfect. The LED-stripe is working just as it should. Thank you for all help.
For you who intend to use MOSFETs I can recommend this shield i found: http://www.robotshop.com/eu/productinfo.aspx?pc=RB-Spa-505&lang=en-US
I´ve ordered one of those for "integration" of the FETs to the Arduino.
I also bought a Cupperhead WiFi-Shield. Next step ahead.